During the crucifixion scene, after the PFJ sings "For He's a Jolly Good Fellow", a very obvious double for John Cleese is playing "Reg" among the PFJ when Cleese enters the scene as the Centurion, looking to free Brian.
When the Suicide Squad arrives during the crucifixion scene, Otto's first line is clearly dubbed. An earlier scene featuring the Suicide Squad was cut, so Michael Palin needed a different line to introduce them.
When the Centurion corrects Brian's slogan, "Romanes Eunt Domus", he says Domum is the locative case, which would be Domi. It's actually the accusative of place, which drops the preposition Ad from Ad Domum. However, the resulting sentence, "Romani Ite Domum", is correct.
When Michael Palin turns around and walks past the two guards to the one standing behind them to say Biggus Dickus to him too, a stage hand is on the right sorting out the contents of a bowl or something. His clothes look contemporary 1970's not Roman era - possibly from a rehearsal scene put in after all the useless re-takes due to Michael Palin giggling himself during it - obvious edits are apparent.
According to the caption text, Brian meets the People's Front of Judea for the first time in the Colosseum in Jerusalem. In fact, the only amphitheater known as the Colosseum is the big one in Rome, officially called the Amfitheatrum Flavium.
Pontius Pilate is portrayed as having a palace in Jerusalem. Although one would easily assume this, due to his role in the New Testament, he actually resided in Caesarea, which was the Roman capital of the Judean province. There are historical mentions of Pilate visiting Jerusalem, but he never lived there.
A Roman centurion in full dress would be recognizable by 3 things: greaves covering his shins and knees, a vine in his hand and especially a helmet with the crest positioned from left to right. Cleese's centurion is wearing none of these badges of rank. His helmet is in fact more like that of a Roman general.
The goof items below may give away important plot points.
When Brian climbs from the crashed spaceship, a spectator says, "You lucky bastard" but his lips clearly say "You jammy bastard". "Jammy" is a very English word, and probably wouldn't make much sense to an international audience.