TL;DR Version:
There are some significant problems with the APA's claim in 2005 that there are no negative effects. Further research (with larger sample sizes, more representative participants, more outcomes analyzed, and longer-running) is necessary to determine if there are negative effects.
There's a good paper titled "Same-Sex Parenting and Children’s Outcomes: A Closer Examination of the American Psychological Association’s Brief on Lesbian and Gay Parenting". They give a pretty good summary of what they are looking at:
The overarching question of this paper is: Are the conclusions of the research presented in the 2005 APA Brief on “Lesbian and Gay Parenting” valid and precise, based on the cited scientific evidence? In the present paper, seven questions are posed, examined, and addressed:
(1) How culturally, ethnically, and economically diverse were the gay/lesbian households in the published literature behind the APA Brief?
(2) How many studies of gay/lesbian parents had no heterosexual comparison group?
(3) When there were comparison groups, which groups were compared?
(4) Does a scientifically-viable study exist to contradict the APA’s published
statement that "not a single study has found children of lesbian or gay parents
to be disadvantaged"?
(5) What types of outcomes have been investigated?
(6) What do we know about the long-term outcomes of children of lesbian and
gay parents?
(7) Have the studies in this area committed the type II error and prematurely
concluded that heterosexual couples and gay and lesbian couples produce similar parental outcomes?
The 2005 APA Brief in question states that
Not a single study has found children of lesbian or gay parents to be disadvantaged in any significant respect relative to children of heterosexual parents.
In short, the paper points out multiple significant flaws in the research referenced by that brief. The paper does not question the validity of the research done, but it does show how we should be highly skeptical of the claim made by the APA until further research has been done.
Regarding what the paper found for each of the seven questions:
In summary response to Question 1 ("How culturally, ethnically, and
economically diverse were the gay/lesbian households in the published literature behind the APA Brief?"), the reader may ascertain that none of the cited articles (pp. 23–45) focus on African-American, Latino, or Asian-American families. Further, many studies do not include any minority individuals or families. Finally, comparison studies on children of gay fathers were almost non-existent as well. By their own reports, social researchers examining same-sex parenting have repeatedly selected non-representative, homogeneous samples of privileged lesbian mothers to represent all same-sex parents. This pattern across three decades of research raises significant questions regarding lack of diversity and lack of generalizability in the same-sex parenting studies.
How many studies of gay/lesbian parents had no heterosexual comparison group? (This is actually the response for question two)
Of the 59 publications cited by the APA in the annotated bibliography section entitled ―Empirical Studies Specifically Related to Lesbian and Gay Parents and Their Children‖ (pp. 23–45), 33 involved a heterosexual comparison group. In direct response to Question 2, 26 (44.1 percent) of the studies on same-sex parenting did not include a heterosexual control group. In well-conducted science, it is important to have a clear comparison group before drawing conclusions regarding differences or the lack thereof. We see that nearly half of the ―Empirical Studies Specifically Related to Lesbian and Gay Parents and Their Children‖ referenced in the APA Brief allowed no basis for
comparison between these two groups (see Table A). To proceed with precision, this fact does not negate the APA claim. It does, however, dilute it considerably as we are left with not 59, but 33, studies with heterosexual comparison groups.
When there were comparison groups, which groups were compared?
Because children in marriage-based intact families have historically fared better than children in cohabiting, divorced, step, or single-parent families on the above outcomes, the question of what "groups" researchers selected to represent heterosexual parents in the same-sex parenting studies becomes critical.
...
In total, in at least 13 of the 33 comparison studies listed in the APA Brief’s list of "Empirical Studies" (pp. 23–45) that include heterosexual comparison groups, the researchers explicitly sampled "single parents" as representatives for heterosexual parents. The repeated (and perhaps even modal) selection of single-parent families as a comparison heterosexual-parent group is noteworthy, given that a nonpartisan Child Trends (2002) review has stated that "children in single-parent families are more likely to have problems than are children who live in intact families headed by two biological parents."
...
As we return to the APA’s section of 33 published "Empirical Studies" (pp. 23– 45) that directly involve heterosexual comparison groups, we see that the repeated, and perhaps modal, practice of same-sex parenting researchers has been to use single parents as heterosexual representatives. Nebulously defined "mothers" and "couples" are frequently used as heterosexual comparison groups, but only in rare cases are explicitly intact, marriage-based families used as the group representing heterosexual parents. This is important because the intact, marriage-based family is the family form consistently associated with best children’s outcomes in large-scale research.
In other words, it appears much of the research has found children raised by homosexual parents to be comparable in outcomes to children raised in conditions known to be sub-optimal.
Question 4 asked: Does a scientifically viable study exist to contradict the APA’s published statement that "not a single study has found children of lesbian or gay parents to be disadvantaged"? The answer is yes. Sarantakos (1996) controlled for "education, occupation, and socio-economic status" and then, based on teacher reports, compared marriage-based families with homosexual families and found nine significant differences—with children from marriage-based families rating higher in eight areas. By objective standards, compared with the studies cited by the APA Brief, the Sarantakos study was:
a) The largest study to examine children’s outcomes,
b) One of the most comparative (only about five other studies used three
comparison groups), and
c) Perhaps the most comprehensively triangulated study (five data sources)
conducted on same-sex parenting.
Accordingly, this study deserves the attention of scientists interested in the question of homosexual and heterosexual parenting, rather than the dismissal it received from APA. As we conclude the examination of Question 4, let us review a portion of APA’s
published negation of Sarantakos’ study:
[Children Australia, the journal where the article was published] cannot be
considered a source upon which one should rely for understanding the state of
scientific knowledge in this field, particularly when the results contradict
those that have been repeatedly replicated in studies published in better
known scientific journals.
Patterson and the APA dismissed the Sarantakos study, in part, because it contradicted the "no significant difference" findings that had been "repeatedly replicated in studies published in better known scientific journals." For other scientists, however, the salient point behind Sarantakos’ findings is that the novel comparison group of marriage-based families introduced significant differences in children’s outcomes (as opposed to the recurring "no difference" finding with single-mother and "couple" samples). Additional studies with intact, marriage-based families as the heterosexual comparison group are conspicuously rare in the APA Brief’s list of "Empirical Studies Specifically Related to Lesbian and Gay Parents and Their Children" (pp. 23–45).
In response to the present article’s Question 5 (what types of outcomes have been investigated for children of gay/lesbian families?), it may be concluded: In the same-sex parenting research that undergirded the 2005 APA Brief, it appears that gender-related outcomes were the dominant research concern, to the neglect of other important outcomes. To be more precise, Table A lists several categories of information regarding 59 published empirical studies; one of these categories is the "outcome studied." More than 20 studies have examined gender-related outcomes, but there was a dearth of peer-reviewed journal articles from which to form science-based conclusions in myriad areas of societal concern including: intergenerational poverty, criminality, college education and/or labor force contribution, drug/alcohol abuse, suicide, sexual activity and early childbearing, and eventual divorce as adults.
Did any peer-reviewed, same-sex parenting study cited by the 2005 APA Brief (pp. 23–45) track the societally significant long-term outcomes into adulthood? No.
Is it possible that "the major impact" of same-sex parenting might "not occur during childhood or adolescence...[and that it will rise] in adulthood as serious romantic relationships move center stage"? Is it possible that "when it comes time to choose a life mate and build a new family" that the effects of same-sex parenting will similarly "crescendo" as they did in Wallerstein’s study? It is possible.
From a scientific perspective, the unfortunate answer to the question regarding the long-term (i.e., adult) outcomes of lesbian and gay parenting is that we have no empirical basis for responding, because not a single peer-reviewed comparison study has followed same-sex parented children across time and into mid-adulthood.
Have the studies in this area committed the Type II error?
Same-sex parenting studies have not employed large enough samples to overcome the possibility, or probability, of the Type II error, thereby "substantially increasing [the] likelihood" of failing to find differences. Further, significant critiques provided by social research methodology specialists Lerner and Nagai (2001) were not cited in the 2005 APA Brief. If the conclusion to be drawn is that there are no parenting differences between same-sex and heterosexual couples, such a conclusion cannot be drawn at the present time, given this problem with the Type II error, pervasive in the same-sex parenting literature.
The APA Publication Manual urges researchers to "take seriously the statistical power considerations" and "routinely provide evidence" of adequate statistical power and effect sizes, however, a review of the 59 articles cited in the APA Brief (pp. 23-45), revealed that only a few complied. Further examination indicated that of the comparison studies, zero studies reached the "minimum requirement" of 393 to detect a small effect size. Indeed, only two comparison studies reached half of the minimum requirement.
Also, here's their overall conclusion:
We now return to the overarching question of this paper: Are we witnessing the emergence of a new family form that (unlike cohabiting, divorced, or single-parent families) provides a context for children that is equivalent to the intact family? Even after an extensive reading of the same-sex parenting literature, the author cannot offer a high confidence, data-based "yes" or "no" response to this question. The data are insufficient to support a strong claim either way, and thus insufficient to produce a definitive binary statement. Such a statement would not be grounded in science. Representative, large- sample studies are needed—many of them, including high quality longitudinal studies (i.e., Table B). Although some same-sex opponents have made "egregious overstatements" and, conversely, some same-sex parenting researchers seem to have implicitly contended for an "exceptionally clear" verdict of "no difference" between same-sex and heterosexual parents since 1992, a closer examination leads to the conclusion that strong assertions, including those made by the APA, were not empirically warranted.
The scientific conclusions in this domain will be clearer as researchers: (a) move from small convenience samples to larger nationally representative samples, (b) increasingly examine critical societal and economic concerns that emerge during adolescence and adulthood, (c) include more diverse same-sex families (e.g., gay fathers, racial minorities, and those without middle-high socioeconomic status), (d) include intact, marriage-based heterosexual families as comparison groups, and (e) acknowledge and respond to experts’ methodological critiques in the effort to refine and add validity and rigor to findings. In connection with this latter point, it is particularly vital that statistical power no longer be ignored. Taking these steps will help lead the field towards more nuanced and scientifically informed responses to significant questions affecting families and children.
Update:
Here are two studies that show negative effects. They attempt to use more random samples in order to avoid self-selection bias. Neither can conclusively say what is causing the negative effects - from the former:
Although the findings reported herein may be explicable in part by a variety of forces uniquely problematic for child development in lesbian and gay families—including a lack of social support for parents, stress exposure resulting from persistent stigma, and modest or absent legal security for their parental and romantic relationship statuses—the empirical claim that no notable differences exist must go. While it is certainly accurate to affirm that sexual orientation or parental sexual behavior need have nothing to do with the ability to be a good, effective parent, the data evaluated herein using population-based estimates drawn from a large, nationally-representative sample of young Americans suggest that it may affect the reality of family experiences among a significant number.