The Spanish Inquisition - S2-E2
Revealing mistake: At the very end when The Spanish Inquisition bursts into the courtroom, you can see that Biggles is not played by Terry Jones (as he is playing the accused judge in the court sketch).
The War Against Pornography - S3-E6
Revealing mistake: When John Cleese (as Long John Silver) falls over after being shot with a tranquilizer dart, you can see his real leg, which was tucked behind him when using the peg leg. (00:20:10)
Revealing mistake: The Italian evening class runs from 7 to 8 PM. The clock at the back of the classroom reads 10 to 2.
Revealing mistake: Near the end of the Bishop sketch, when they use the man as a battering ram, you can see the entire wall behind them tip as they smash through the door.
Scott of the Antarctic - S2-E10
Revealing mistake: In the last shot, the familiar 16 tons weight is broken at the top, showing that it is in fact not a solid weight, but a hollow box.
Chosen answer: The song you talk of was originally a poem by William Blake called 'Jerusalem'. It speaks of the possibility of Jesus having visited England. The poem has four verses but you only ever hear the Monty Python boys sing the first one which goes, "And did those feet in ancient time/Walk upon England's mountains green/And was the holy Lamb of God/On England's pleasant pastures seen?" If there's any sort of in-joke connected to it's use, I'm not aware of it. It seemed to just be the standard song/hymn they used when a song was needed that wasn't sketch specific. Some of the sketches it appeared in were 'Salvation Fuzz/Church Police', 'Buying a Bed' and 'The Art Gallery Sketch'. Something that may be relevant, though, is that the only one who was present every time it was sung was Eric Idle. Perhaps he just liked it?