A story in Slate, "Thimerosal on Trial: The theory that vaccines cause autism goes to court," by Arthur Allen, introduced me to the vaccine court. Actually, it merely used the expression, assuming I'd know what it was, and I had to turn to Wikipedia for clarification. Seems that the U.S. Court of Federal Claims was given that label after the 1986 National Childhood Vaccine Injury Act created a sort of no-fault system protecting vaccine makers from full tortious liability and directing all lawsuits into that court. At present there are nearly 5000 claims about to be heard on the question of whether the U.S. vaccine program harmed the litigants' children, in particular by causing autism. There is an allegation that thimserosal, a mercury-containing preservative once used to protect vaccines, causes autism, though scientific evidence would seem to be lacking for this claim.
The United States Court of Federal Claims is an interesting institution in a number of ways (see the description by the current presiding Chief Judge), including the fact that the 16 judges sit for 15 years, rather than life and an unusual close relationship to Congress.
Clearly the vaccine work dominates the court, because they're managed by the (congressionally-created) Office of Special Masters comprising 8 special masters who sit for terms of 4 years.