My favourite part of the show is near the end, when everyone gathers in front of the fire to sing Christmas Carols: Statler & Waldorf singing I Heard The Bells On Christmas Day is a highlight for me, and Kermit and Robin having another duet on It's In Every One Of Us To Be Wise, which is actually a call back to an earlier Muppet Christmas special, when it was sung by John Denver. I've never seen that one, but had- oh heck, still have- the CD of music from it. The Muppets have always had great music and great guests.
Another nice touch is that we get to briefly see Jim Henson at the end of the special, in the kitchen washing dishes. This wasn't very long before his death, so that adds another touch of nostalgia to the show, which has just hit all the feels by having the entire cast sing Together At Christmas ("Old Friends, new friends, home with the family, we'll be together at Christmas..."). Weird how the one or two Hallmark Christmas movies my sisters have talked me into watching have left me cold eyed and cold hearted, but this scene with a bunch of puppets can make me a little misty-eyed. Of course, it helps that I'm a sucker for family sing-alongs... gathering around the piano with multiple generations of the clan is something I love about our get togethers.
Unfortunately, A Muppet Family Christmas is not available in its entirety to purchase; I think it may be on Disney+, but if it is, it's had some of the songs cut out because of copyright issues. The complete show can be found in certain places online (cough, cough YouTube)... or so I've heard.