Crowning Moment of Awesome: The whole special, really. What kid didn't get a kick out of seeing their favorite characters from three different shows (four if you wanna count the Muppet Babies home movies segment) all in one special?
"Funny Aneurysm" Moment: It's more "sadly poignant" than "painfully cringe-worthy", but Jim Henson making a Christmas cameo alongside so many of his creations gained a lot more emotional gravitas in the light of his death just three years after this special aired.
Memetic Mutation: At least in the Muppet fandom, virtually every line is quotable.
"Look out for the icy patch!"
"The dog is not the turkey! The turkey's the turkey, you turkey!"
"We'd love to see your act!" "In fact, we'd hate to miss your act!" "In fact, we'd love to hate your act!"
Tear Jerker: Jim Henson's brief cameo at the end. We miss you, Jim...
Not to mention seeing Richard Hunt's main Muppet characters together (as he succumbed to HIV in 1992) and, later, all the numerousroles played by Jerry Nelson, who passed away in 2012.
To a lesser extent, Elmo's appearance in the Muppet crowd at the end (Kevin Clash is still very much alive as of this writing, but he was forced to resign from the character due to abuse allegations in 2012).
Along with all of the above, Doc's whole role in the special becomes bittersweet after Gerry Parkes' 2014 passing.
Of course, seeing all the Muppets together like this is a happy tearjerker.
Big Bird and Swedish Chef singing "Merry Christmas to You", which even brings the Chef to tears.