Actors were required to "hydrate" every twenty minutes while on location in the desert. Huge, "multicolored" blocks of ice were brought in from Tel Aviv for this process.
After Jesus finds his apostles asleep, the camera cranes up next to the leaves of a tree. At one point (about 1:00:48 on the DVD) one of the tree twigs swings back and forth rather unnaturally, indicating that the camera has brushed against it in the process of going by.
During the opening of the final song "Jesus Christ Superstar", after Judas steps off the chain the lipsync is out of time with the song. It's corrected after the first cutaway.
Peter: I think you've made your point now! You've even gone a bit too far to get the message home! Before it gets too frightening we ought to call a halt. Oh, could we start again, please?