First off, the lead author of the study, Andrew Wakefield, was not a pediatrician who specialized in the treatment of children, nor was he an immunologist, who specializes in studying and treating the immune system. He was a gastroenterologist, who was consulted over some digestive disorders.
Second, he based his research on a study of only 12 children whom he treated. Yes, you read that correctly. Twelve kids. Not 200, or 6,000, or 15,000. Twelve. And that was his sole study group. There was no control group with which to compare results.
Third, he collected blood specimens from random children whom he invited to his son's birthday party, and paid them 5 pounds each for their blood. He did not obtain informed consent from the kids or their parents, a major violation of medical ethics and research protocols.
Fourth, he accepted over 400,000 pounds in payment from a group of attorneys retained by parents groups to sue the pharmaceutical companies that manufacture vaccines.
Fifth, he now blames thimerosol and the minute levels of ethyl mercury it contained as causes of autism, but in his original paper, he never mentioned thimerosol or mercury, mainly because the MMR vaccine he was blaming for autism did not even contain thimerosol.
Is this enough? Or do you need more data? If so, check out http://archpsyc.ama-assn.org/cgi/content/full/65/1/19.