Emmet Otter's Jugband Christmas might be my favorite Christmas special (that's actually of quality). I remember first seeing it at a neighbor's house because he had HBO and shouted across to my window that the Muppets were on TV. Kermit the Frog introduced the story, based on the book by by Russell Hoban and Lillian Hoban, about a poor mother and son who trade their livelihoods to enter a battle of the bands — unbeknownst to each other — and win money to buy the other a nice Christmas present. It's warm, simple and earnest.
But it also features some great outtakes. The Jim Henson Company posted a selection of these to their YouTube channel and it's delightful to see puppeteers like Frank Oz, Jerry Nelson and Jim Henson himself both stay in character and occasionally break when props fail to work or lines are flubbed.