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 the Gladiator has a heart attack in front of the entrance gate to the arena. A high ranked Roman then makes the comment absolutely dreadful. Next scene the gladiator is no longer in front of the entrance gate. Note, the gladiator who suffers the heart attack was called a Hoplomachus gladiator.
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.
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.
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.
When Judith interrupts the PFJ to tell them Brian is going to be crucified, Stan aka Loretta is writing the meeting minutes from right to left as a Jewish writer would but he is writing each word from left to right then moving his hand to the left of what he is written not each word right to left as a Jewish writer would write.
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.
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.