Continuity mistake: During an early scene, the People's Front of Judea are conversing while Brian is selling food. The man to the right of Reg has no tear in his shirt collar at the beginning of the scene. Once Brian approaches them his shirt collar has a significant tear that wasn't there before. (00:21:20)
Continuity mistake: The cross carried to the crucifixion scene by the Saintly Passer-by looks nothing like the one they crucify him on. The cross bar is a narrow pole, and the upright is much smaller than the one he ends up on. They do not crucify him on a different cross - he is roughly pushed down on the flimsy prop cross he carried, then instantly is hauled upright on a sturdy one.
Continuity mistake: After Brian is caught by the alien spacecraft, his yamulka is in front of his hairline. But, once the camera pulls away to show the aliens his yamulka is placed very far back on his head. (00:43:09)