"This is the face of a murderer, not our Lord!"
-Sergio Leone, filmmaker
In this film, Jesus is portrayed as having many different very human feelings. These feelings such as hatred, jealousy and apathy, along with Willem Dafoe's "unique" physical appearance all give (to some) a too realistic interpretation of what Jesus Christ may been like.
Many of the right wing Christians who hated this film would have preferred a more docile loving Jesus. A man who curses objects that infuriate him and is visibly moved by a nude Mary Magdalene is in some ways too much man and not enough God.
There are many more controversial elements to this Jesus that fuel the fire of opposition. At the beginning of the film it is revealed that Jesus is working as a carpenter, making crosses for the Romans to crucify people on. This prompts the character of Judas to scoff, "I struggle, you collaborate." (More on Judas's opinion of Jesus in "Judas Iscariot", found above).
Jesus does not handle the pressure that God has put upon him well. When God's talks to him he is in physical pain and he is very conflicted with his decisions. He compares the pain to claws in his brain.
He takes God's will as wanting to "push [him] over" [a cliff] and that his faith is dominated by how afraid he is not to obey. He sees women and blushes because he wants them but knows he cannot have them (more on sexual temptation in "Jesus and his Sexual Desire"). He is proud and pride is a sin. He does not kill, fight or steal yet only because he is afraid to do these things. He exclaims "My God is fear!"
These are emotions every man may get when loaded with such a burden. Yet since this movie shows Christ dealing with it like a human and not like a God, it was thought of as an atrocity.