The film shows the people trying to get Pilate to free people with R's in their name, so they can laugh at his speech impediment. In the Bible, who do they ask Pilate to free instead of Jesus? Barabbas.
The "Blessed are the Cheesemakers" joke becomes even funnier when you found out that part of Jerusalem, at that time, was called The Valley of the Cheesemakers.
Brian gets abducted by aliens. There are conspiracy theorists who point out hypothetical UFOs in the backgrounds of paintings of Jesus, and there is also a belief that Jesus himself was an alien or alien/human hybrid.
In the "He's not the Messiah, he's a very naughty boy!" scene, Brian's mother says that she'll let the crowd see him for one minute. When she grabs him by the ear and pulls him back inside, it's been almost exactly one minute.
The giant head that causes all the destruction in the opening credits sequence is taken from a bust of Constantine the Great, the first Roman emperor to fully embrace Christianity.