Perhaps the ultimate example is "Oh Dance, Baby", where Bret starts singing karaoke, entirely in Korean, about the difficulty of being in love. Or something.
Interestingly, Mushroom Samba song Prince of Parties is not one: in fact, it is actually probably the only song in the series that is directly referenced in a later episode: "If you party with the party prince, you get two complimentary after-dinner mints!" sings Bret, wearing the costume from Prince of Parties, in the second-season song Sugarlumps.
That's a BLAM referencing another BLAM... so meta...
Alternatively, all the sudden song numbers exist in the same alternate reality...
Ear Worm: Too many to list. Everyone has their favourites.
Ensemble Darkhorse: Murray. He's probably the only truly sympathetic character.
Fridge Brilliance: In the song "Hurt Feelings", Jemaine laments about how his family forgot to call him on his birthday. His next line in the song is "The day after my birthday is not my birthday, mom." At first, this just seems tragically hilarious. However, when you consider time zones and the fact that Jemaine's mom most likely lives in New Zealand, it makes perfect sense that she would call him the day after his birthday. It was his birthday in New Zealand.
No, it's the other way around. If it's the 10th in New Zealand, it's the 9th in the USA. To ring someone on their birthday in the USA you have to ring them the day after their birthday in New Zealand.
Harsher in Hindsight: Jemaine finally realizes that the whole Garfunkel thing was really kinky.