Channel Hop: After airing on CBS for 36 straight years, the special moved to its present network home of ABC in 2001.
Edited for Syndication: For most of its run on CBS, as well as its first VHS release, the scene of the kids throwing snowballs at the can on the fence was cut out. It was restored for its second VHS release and was reinstated in network broadcasts in 1997 (with the can redesigned).
Executive Meddling: CBS executives had some issues with the special as it was originally put together. They objected to:
The Scripture quotation that Linus recites to explain the meaning of Christmas.
Using actual children to voice the Peanuts characters.
In other words, nearly everything that makes this program a timeless classic. Fortunately, Schulz and Melendez stuck by their guns and were vindicated the moment it aired.
Magnum Opus Dissonance: Nobody behind the project thought it was any good when they finished; Lee Mendelson and the rest of the team felt they "ruined Charlie Brown" when they looked at the final cut before it aired.
It apparently took a while for Charles Schulz himself to realize how iconic this special had become. In the late 1980s he fretted that he hadn't produced his "own Citizen Kane" and invested a good deal of time and money on his intended masterpiece, the flop live-action/animated combo It's The Girl in the Red Truck, Charlie Brown. Any fan could've told him he'd already made his Citizen Kane way back in 1965. (Ironically, Orson Welles didn't consider the actual Citizen Kane to be his masterpiece.)
Network to the Rescue: CBS made some cuts to the special in the '90s because shows made more room for commercials by then (see Edited for Syndication above). When ABC acquired the rights in 2001, they blocked out a full hour for the special so that it could run uncut, commissioning Charlie Brown's Christmas Tales to fill the extra time. (ABC does air cut half-hour versions some years, but the full version will be shown at some point during the season.)
What Could Have Been: Apparently when the project was started, the network just wanted this to be a regular goofy Peanuts short that just happened to take place at Christmas time. They weren't expecting the shots at commercialism and Linus' big speech. It's a good thing the special didn't go this direction, too, because it wouldn't be nearly so memorable otherwise.