TotP had many infamous moments during its long run, but few were more excruciating that when All Above Eve were on this 1988 show to perform the glorious Martha's Harbour. As quickly became clear, the band couldn't hear the audio at all, which led to this... you had to feel for them.
And many bands have taken the piss out of the show while on air, but Nirvana's performance of Smells Like Teen Spirit - sung live by Cobain - was a benchmarker as Kurt sang in completely the wrong octave.
What else you got?