There has been a great deal of speculation about autism and a possible link to certain vaccines containing mercury - but quite a few studies have been done, and no on has ever found a causative link. The first symptoms of autism generally occur at the same time as a particular set of common vaccinations - but while correlation has been found (onset occurs shortly after the vaccination) causation has not (the vaccines have not been shown to trigger autism, just to be diagnosed shortly after). Children receiving the same vaccinations, but without the thimerisal (a preservative suspected of causing autism), or not receiving the vaccinations at all, have similar rates of diagnoses of autism.
Would that it were that simple...