OK, this has got to stop.
Frogster, I can understand where you are coming from but I ultimately disagree. The Rainbow Connection has been covered in pretty much every style possible, it can be in this movie. I'm sure the Moopets' cover is done for laughs and must be short. I wouldn't worry too much about it. "You'll Never Walk Alone" seems like a pretty untouchable song thanks to Jerry Lewis, but people still cover it.
Some of the songs seem a bit random for me, but they are there for a reason. I'm going to assume "Me and Julio Down by the Schoolyard" will play when Gary visits Mary at work (she is a teacher after all).