These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
There is, actually, a full soundtrack of the songs that the Band With Rocks In did.
Terry Pratchett himself mentioned in an interview how impressed he was with the cartoon's soundtrack.
Fridge Brilliance: At the end, Imp turns out to have reappeared cooking fish and chips at a hot food shop. This is the same sort of work that Death himself was doing when he felt happiness for the first time in Mort. He didn't just spare Imp's life, he found him one that would allow Susan to meet him and that he thought would make Imp happy! Awwww....
In the animated adaptation, the song "Good Lovin'" contains the lines: "I know the road and I'm in command/ We're gonna hit the heights." This seems to foreshadow the climax, where the Band's cart goes over the edge of the same high mountain road where Mort and Ysabell fell to their death.
"Funny Aneurysm" Moment: That whole Klatchian Foreign Legion bit is sure less funny now, in light of Terry Pratchett's..."embuggerance".
The actions The Musicians' Guild take in trying to stop music from being given away for free seems to be predictive of the current antics of the RIAA. Well, except the RIAA haven't tried to have anyone killed. (So far as we know).
They did the same thing at the birth of radio, and so did the Musician's Union in the UK. Since Pratchett is a British author old enough to remember this, it's most likely a reference to the MU's opposition to recorded music being played in public venues.
Narm: It becomes a bit harder to feel sad in the scene where the band die, due to Susan suddenly screaming "NOOOOOOOOOO!" to the heavens.