Is the picture anti-Semitic? Well, it takes many of the anti-Jewish elements from the New Testament and arranges them in such a way that it heightens Jewish guilt. And no, I don't agree that saying there are anti-Jewish elements in the New Testament means I'm saying that it's is anti-Semitic; there's more to the books than that. There IS fuel in the gospels to create something anti-Semitic, something which the Vatican explicitly warns against and posted guidelines about, and I think that's what happened to Gibson's movie, intentionally on his part or not. Catholics who believe in the Vatican and in Vatican 2 (which, whether you're a believer or not, has plenty of sensible things to say, especially on Christian-Jewish relations) better take this movie with a huge block of salt.
I say "intentionally or not" because despite the claims that it's from the bible, Gibson does take images and situations from another book--the visions of Anne Catherine Emmerich, a 17th century nun who WAS anti-Semitic (one of her writings has the claim Jews used the blood of Christian children for "diabolical purposes").
Emmerich is practically the guiding spirit of Gibson's film; the order in which different parts of the gospels have been chosen and arranged are due to Emmerich; the re-jiggering of Pilate's character as a sympathetic and reluctant judge over Jesus is due to Emmerich. As Philip Cunningham, executive director for the Center of Christian-Jewish Learning in Boston College puts it, the picture might as well be called "The Passion according to Anne Catherine Emmerich."