I suppose those people saying proving an arbitrary multithreaded program is thread-safe is impossible are, in a way, correct. An arbitrary multithreaded program, coded without following strict guidelines, simply will have threading bugs, and you can't validly prove something that isn't true.
The trick is not to write an arbitrary program, but one with threading logic simple enough to possibly be correct. This then can be unambiguously validated by a tool.
The best such tool I'm aware of is CheckThread. It works on the basis of either annotations, or xml config files. If you mark a method as '@ThreadSafe' and it isn't, then you get a compile-time error. This is checked by looking at the byte code for thread-unsafe operations, e.g. reads/write sequences on unsynchronised data fields.
It also handles those APIs that require methods to be called on specific threads, e.g. Swing.
It doesn't actually handle deadlocks, but those can be statically eliminated without even requiring annotation, by using a tool such as Jlint. You just need to follow some minimal standards like ensuring locks are acquired according to a DAG, not willy-nilly.