First the anti-Semitism.
I can very well see, very easily and sympathetically see how someone attuned to such matters could find much in the film to critique on this level. I don’t think that every critique of the film’s treatment of Jewish leadership is equivalent to a critique of the Gospels on this score. “Well, he’s just filming what’s in the Gospels.”
What is not clear in this film is the Sanhedrin’s motivation. It seems to me (and maybe I missed something) that two conflicts are conflated in the film: Jesus’ ongoing conflicts with the Pharisees, and then the conflicts in Jerusalem with the Temple leadership. It was not the former that got him crucified, (only John mentions Pharisees has having anything to do with the arrest of Jesus) it was the latter, and the driving force in that was political – fear that if a popular movement arose around Jesus as messiah, the Romans would brutally put it down. There is absolutely no sense of this in Gibson’s film, at least as far as I could discern, and that is a crucial, unfortunate omission.
So while I do think that there’s been some manufactured hand-wringing about this aspect of this film, there are good reasons for finding flaws in the treatment of the material, because on this point, it just doesn’t give the full picture.