I know this film is controversial, and I've heard a lot of stuff about it. So I thought I'd watch it and see what I thought. Here's an outline of the plot.
What is meant to be controversial about this film is the way that Jesus is tempted sexually - specifically to come down from the cross, enjoy a "normal" life, first with Mary Magdalene, then with Mary of Bethany (and Martha on the side with the argument that "there is only one woman in the world"). I don't have a problem with the idea that Jesus was tempted to avoid the cross, to live a normal life, to settle down and have kids, even to sleep with multiple women. If Jesus was "tempted in every way, just as we are", that temptation might well have included that sort of thing.
I guess the whole Judas storyline, with Judas being Jesus' closest disciple, the only one whom Jesus trusts enough to ask him to betray him, is also controversial. It doesn't fit with Judas being the one who was embezzling funds from Jesus though, so I don't tend to agree with it.
The film is meant to be struggling with the tension between the divinity of Christ and his humanity. But where the film goes wrong isn't on overemphasising the humanity of Jesus, but underemphasising his divinity. So the film presents a Jesus who thinks at one point that the voices telling him he is the Son of God are demonic, for example, and who doubts his own Messiahship for almost all the film. Despite what the Wikipedia page says, this Jesus frequently refers to stuff he's done wrong, so seems to be sinful too, as well as a pantheist. The Jesus of the film isn't a Jesus who could inspire his followers (not just Paul - the people who knew him during his life) to write the gospels.
This tension gets recognised as the film goes on. So in the long vision/temptation sequence where Jesus is tempted to avoid the cross, he meets Paul who is preaching Christianity and who ends up rejecting him because the Christ of faith is far more useful to him than the Jesus of history who (in this case) wasn't crucified. That just doesn't work. It doesn't explain Paul's conversion, or his willingness to die for what he taught, as well as using ideas that just didn't appear for another 1800 years or so.
In fact, in the film, the only way that Jesus is able to go through with the crucifixion is after the temptation sequence (and ironically after Judas accuses him of being a traitor) when he realises that he really is the Messiah and he really does have to die. The problem is that in order to inspire the reaction he clearly did inspire in those around him, he needs to have been less of a bumbling failure for the rest of his ministry.
I've studied a bit of patristics this term, which is a lot of debates in the early church, mostly about how best to explain who Jesus was. They concluded that Jesus was fully man and fully God from the start because that was the only conclusion that fit their historical data. It doesn't fit this film.