Bert and Ernie getting gifts for one another was a take on the 1905 Christmas story, "The Gift of the Magi," b O. Henry. In that story, a poor young couple each sell their most valuable possessions in order to afford Christmas gifts for one another; the husband sells his pocket watch to buy his wife a set of fine combs for her hair, while the wife sells her hair to a hairdresser to buy her husband a fob chain for his pocket watch. The original story ends with the gifts that were sacrificed for being virtually useless to the recipient (though they show the dedication the couple have to one another). There was no Mr. Hooper-type character to save the day.
The Christmas Eve on Sesame Street Album was nominated for a Grammy. It featured several songs from the televised special along with narration.
For Kermit's appearance in this special, the puppet from The Muppet Movie was used. Around that time, the company that made the green cloth that were originally made for Kermit went out of business. While CTW usually had a series of Kermit puppets built at the same time specifically for Sesame Street remained in use on the show until 1981, the 1978 puppet was used here.
When aired by Nickelodeon in 1994, "I Hate Christmas" was cut. While later airings until 2001, the song remained, but Keep Christmas with You was cut.
Big Bird worries that Santa is stuck in a chimney somewhere or "stacked over Kennedy." Kennedy would be JFK International Airport in New York (Sesame Street is a fictional location in NY). "Stacking" refers to a holding pattern wherein pilots circle a radio beacon at assigned altitudes, done when they are not permitted to land (usually due to weather conditions).