This Wikipedia page contains all you ever wanted to know on the controversy and has 99 citations, a lot of which are to peer-reviewed material and meta-studies.
In particular, the section "Clinical Trials", says clearly that the safety of silver fillings is disputed:
Conducted trials and their conclusions
The proper interpretation of the data on hand is, to date, controversial. The vast majority of past studies have concluded, not without controversy, that amalgams are safe. However, although the vast majority of patients with amalgam fillings are exposed to levels too low to pose a risk to health, many pateints (i.e. those in the upper 99.9 percentile) exhibit urine test results which are comparable to the maximum allowable legal limits for long-term work place (occupational) safety. Two recent randomized clinical trials in children discovered no statistically significant differences in adverse neuropsychological or renal effects observed over the five-year period in children whose caries were restored using dental amalgam or composite materials. In contrast, one study showed a trend of higher dental treatment need later in children with composite dental fillings, and thus, claimed that amalgam fillings are more durable. However, the other study (published in JAMA) cites increased mercury blood levels in children with amalgam fillings. The study states, "during follow-up [blood mercury levels were] 1.0 to 1.5 μg higher in the amalgam group than in the composite group." EPA considers high blood mercury levels to be harmful to the fetus, and also states that "exposure at high levels can harm the brain, heart, kidneys, lungs, and immune system of people of all ages." Currently, EPA has set the "safe" mercury exposure level to be at 5.8 μg (micrograms) of mercury per one liter of blood. While mercury fillings themselves do not increase mercury levels above "safe" levels, they have been shown to contribute to such increase. However, such studies were unable to find any negative neurobehavioral effects.
During the FDA's December 13–14, 2010 CDHR panel review of the International Academy of Oral Medicine and Toxicology's request for reconsideration to the classification of amalgam, neurologists questioned the type of neurobehavorial tests and the unethical nature of a prospective trial looking for brain damage in children. Furthermore, evidence was presented by the Geier's that further analysis of the data found that an unusual porphyrin called Coproporphyrinogen indicative of pathophysiology (harm) was found in a dose response relationship to the number and size of amalgams placed, thus calling into question the claim that no injury had occurred.
As a result of a lawsuit, a fund was developed to research amalgam-related illness, and a clinical trial evaluating the effect of removing amalgam was published in 2008. The trial found that all groups had improved symptoms, including a group where the participants were treated with a "biological detoxification" therapy and dental amalgam was not removed.Follow-up of a clinical trial was published in 2010.
Let me show some studies here (both from the Wikipedia article and from looking around), as you can see, they do not seem to agree very much on the actual effects:
Urinary mercury concentrations associated with dental restorations in adult women aged 16–49 years: United States, 1999–2000
It is estimated that an increase of 1.8 μg/l in the log transformed values for mercury in urine would occur for each 10 dental surfaces restored with amalgam.
Immune Function Effects of Dental Amalgam in Children
These findings suggest that immunotoxic effects of amalgam restorations are minimal and transient in children and most likely do not need to be of concern to practitioners considering the use of this restorative dental material.
Neuropsychological and Renal Effects of Dental Amalgam in Children
In this study, there were no statistically significant differences in adverse neuropsychological or renal effects observed over the 5-year period in children whose caries were restored using dental amalgam or composite materials. Although it is possible that very small IQ effects cannot be ruled out, these findings suggest that the health effects of amalgam restorations in children need not be the basis of treatment decisions when choosing restorative dental materials.
Neurobehavioral effects of dental amalgam in children: a randomized clinical trial.
In this study, children who received dental restorative treatment with amalgam did not, on average, have statistically significant differences in neurobehavioral assessments or in nerve conduction velocity when compared with children who received resin composite materials without amalgam. These findings, combined with the trend of higher treatment need later among those receiving composite, suggest that amalgam should remain a viable dental restorative option for children.
Mercury from dental amalgam: looking beyond the average
In summary, the average mercury dose from amalgam fillings is in most cases below 5 mg per day on average, but the issue of the right tail of the distribution is more important. A substantial number of persons have a mercury uptake from dental amalgam that is higher than should be accepted.
Many of these cases are likely to be found among people with intense chewing gum use.
Neurobehavioral effects from exposure to dental amalgam Hgo: new distinctions between recent exposure and Hg body burden
In conclusion, by using an approach that distinguishes recent Hg exposure from Hg body burden, we have observed subtle associations between Hg and symptoms, mood, motor function, and nonspecific cognitive alterations in task performance in an occupationally exposed group with HgU levels comparable to the general U.S. population. Application of this approach may be particularly useful in defining thresholds of Hgo toxicity and for establishing safe limits of exposure to mercury from dental amalgam material, the restoration itself, diet, and other sources.
Predictors of treatment outcomes after removal of amalgam fillings: associations between subjective symptoms, psychometric variables and mercury levels.
Results contribute some new aspects to the inconsistent findings in the literature with respect to associations between symptoms and subtoxic mercury levels. More emphasis should be placed on exploring individual vulnerability for amalgam sensitivity.
Treatment of health complaints attributed to amalgam
The aim of the present study was to compare the reduction of subjective complaints by 3 treatment strategies in 90 "amalgam patients" whose complaints could not be explained by a medical or psychological disorder. The individuals were randomly assigned either to removal of dental amalgam only (removal group), or removal in combination with a "biological detoxification" therapy with high doses of vitamins and trace elements (removal-plus group), or participation in a health promotion program without removal of dental amalgam (no-removal group). Between baseline and month 12, the sum score of main complaints decreased by 3.5 (SD=2.2) points on average in the removal group as well as in the removal-plus group, and by 2.5 (SD=2.4) points in the no-removal group (p=0.152). Both removal groups showed a significant decrease in steady-state levels of inorganic mercury compared with the no-removal group. Thus, all 3 interventions were associated with clinically relevant improvements.