Enforced Method Acting: 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.
Spike Milligan makes a cameo appearance (he just happened to be around when they were filming... in Tunisia).
One of the guards who finds it wisible when Pontius Pilate mentions his gweat fwiend Biggus Dickus is Hugh Abbott MP.
George Harrison has a brief cameo as "Mr Papadopolous", who owns "The Mount".
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.
It's simple really — Holy Grail is sillier, more random, more madcap and for want of a better word more "Pythonesque", which some people find simply funnier. Life of Brian is arguably the better film and its humour is much more incisively satirical than the outright looney Holy Grail.
Off-the-Shelf FX: The spaceship prop's "exploding" mechanism was powered by exploding cigars and a lightbulb filament (DVD commentary).
Shout-Out: A 'Judith' is an impressively dense patch of pubic hair, according to the 'Roger's Profanisaurus' section of Viz magazine.
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.