An interesting claim which starts with a plausible idea: that CFLs produce transient high-frequency noise in your electrical system. This answer is partial and incomplete but I though some observations were worth reporting in the hope that further investigation by me or others can flesh out the detail.
The website of the firm selling the filters that supposedly fix the problem is the primary place to look for links and references it is here. I'm suspicious already as someone is trying to sell something. The key academic references converge on a single academic (Magda Havas) who has a variety of publications on related topics (but who disavows any interest in their commercial success despite having an apparently close relationship with their inventors as one paper states, for example):
Conflict of Interest
Please note that the author has no vested interest, financial or otherwise, in the commercial devices mentioned in this article.
The author thanks the people who participated in this study; Dave Stetzer and Martin Graham for information about power quality; and reviewers for their critical comments and suggestions.
NB Stetzler and Graham are the designers of the filter sold on the dirty electricity website.
Magda Havas studies are superficially plausible and seem, at least some of the time, to observe proper experimental procedure (though details are often a little light). But the diabetes claim is based on this study Dirty Electricity Elevates Blood Sugar Among Electrically Sensitive Diabetics and May Explain Brittle Diabetes This paper claims:
In an electromagnetically clean environment, Type 1 diabetics require less insulin and Type 2 diabetics have lower levels of plasma glucose.
which appears a clear-cut piece of evidence. But the claim is based on precisely four subjects which casts some doubt on the statistical validity. In fact I'd go as far as saying that to publish a study with this little evidence is a major sign that you don't want to (or can't) produce real evidence.
I'm making a superficial judgement about the body of work without (yet) having time to examine or validate it all, but I'd say this is poor quality science based on the work of a very small number of researchers who don't adopt stringent statistical standards.
There is no plausible mechanism for the effects observed and the observations are not the result of rigorous trials .These claims demand high quality repeatable evidence and that is not what you find on tracing the references here. In fact the site is a cornucopia of references to other emf sensitivity theories many of which have already been dealt with on skeptics.se e.g. here: Are WiFi waves harmful?
So I'm saying the answer is no, CFL's don't harm you via "dirty electricity" unless someone can point me to some serious research that says they do.