Deliberate mistake: Eric Idle's 'Stock Exchange Report' (in Series 3, Show 1) has a very obvious edit in the middle. This is a monologue delivered without cutaways, so the jump in the video tape is very easy to spot. Whether this edit indicates material removed or a simple joining together of two takes is unclear. However, since Idle gets drenched with water at the close of the routine (and given that, under BBC constraints, there was no time for drying out), we can assume that he must have made his fluff quite early on in the piece.
Audio problem: In the 'PC Pan-Am Gives Evidence' sequence (part of Series 3, Show 1), there is a loud, off-camera crash at 16'15", followed by hysterical audience laughter and a Palin visibly trying to stifle a laugh. This is because the heavily-bandaged 'Njorl', who had been replaced at that point by a dummy (enabling his head to be removed in the next scene), fell backwards off the podium, and had to be re-positioned by the crew. Filming presumably stopped, as a cutaway of Njorl appears in the middle of Pan-Am's address. The edit is also very audible, as Palin's speech suddenly plummets in volume.