Accidentally Accurate - the whole shtick about the different anti-Roman groups and their infighting is clearly intended as a Take That against then current leftist groups in the UK, but incidentally the real live anti Roman groups at the time did more infighting than fighting against the Romans. Ultimately this meant that all three Jewish uprisings against the Romans failed precisely because of that We ARE Struggling Together, though the immense military strength of the Roman Empire didn't help either.
Banned in China: The film still remains banned in nations including but not limited to: Bhutan, Oman, Singapore, and South Africa. It used to be banned in Ireland and Norway. Swedish theatres advertised it as "The film so funny they banned it in Norway."
The extras playing the guards in the Biggus Dickus scene were told not to laugh while filming. Thus their desperate attempts to keep a straight face are genuine.
A small one, but in the scene where the crosses are being carried up the hill, the guard (apparently named Parvus) hits Eric Idle's annoying character. It was supposed to be only a tap and not meant to hurt, but the actor was annoyed with him that day and whacked him instead. Eric's brief look of surprise is genuine.
A rare positive example. The original production company canned this movie at the last minute, fearful that the religious subject matter would offend people. So ex-BeatleGeorge Harrison stepped in, paid a few million pounds, and more or less let the Pythons do whatever they wanted... for the sole reason that he was a huge Python fan and wanted to see their next movie. Eric Idle later described it as "the most expensive movie ticket ever purchased."
The one thing they did cut to avoid offending people was a Jewish Nazi-esque character named Otto, who wore a combination Star of David/swastika and wanted to make Israel a racially pure Jewish nation. He shows up at the end as the leader of the "suicide squad" that tries to help the crucified convicts by pointlessly killing themselves on the ground under the crosses.
Magnum Opus Dissonance: The Monty Python crew consider this to be their masterpiece, but most other people say that the less controversial Monty Python and the Holy Grail is the best thing they've made. John Cleese once stated that most people in Great Britain are a fan of Life of Brian, while Americans like Holy Grail better.
Off-the-Shelf FX: The spaceship prop's "exploding" mechanism was powered by exploding cigars and a lightbulb filament.
The scene of all the people trudging uphill to listen to the Sermon on the Mount. It was getting late in the day and the extras all started to leave during a lull in filming and had to be herded back, and it was Eric Idle who noticed that it looked really good and said to turn the cameras on.
The lone man in the "We are all individuals" scene, who plaintively comments "I'm not!"? Yeah, that was this trope. He ended up getting a pay raise to speaking actor for his improv.
Whilst filming the last scene, the actors were all bored and hot sitting up on their crucifixes. So Eric Idle started singing a little ditty. Everyone (but Eric) liked it so much that they decided to use it.
The concept of the film came when Eric Idle said in a post-Holy Grail interview that their next film would be "Jesus Christ: Lust for Glory." Needless to say, the concept went through numerous revisions, including one where Brian was the unknown 13th Apostle, who was always slightly late to important moments of Jesus' life.