Toy Santa's line, "You are a sad, strange little man," is also used by Tim Allen as Buzz Lightyear in Toy Story (1995) Also when the Toy Santa says "I think Santa feels a little Buzz!" is from him being "Buzz Lightyear" in Toy Story.
Scott Calvin starts talking about cars and engines while talking to Carol Newman, and while walking through the toyshop, Santa picks up and tries on a tool belt. These reference to Tim Taylor, Tim Allen's character on Home Improvement (1991).
When Scott captures the Tooth Fairy and tells him he is Santa, The Tooth Fairy, doubting that Scott is Santa Claus, tells him "I know Santa. Santa is a friend of mine, and you sir, are no Santa." This is a parody of Lloyd Bentsen's famous retort to Dan Quayle during the 1988 US Vice Presidential debate.
The line "Quit the chit-chat-Chet" comes directly off a season 1 episode of Tim Allen's Home Improvement (1991) where a man named Chet on the phone babbles too much during a game of "Stump The Tool Man."
Whether intentional or not, Carol Newman is very similar to Jessica from Santa Claus Is Comin' to Town (1970). Like Jessica, she works at a school, is given a doll by Santa, and even shares the same hairstyle and blue eyes.
GOOF: Beginning of the movie it appears that a Coast Guard aircraft almost finds the north pole complex. Except that they report hearing something through SONAR. Although an auditory system, it is used under water, often with a pulse like radar, not air to ground. Also individual asks if it sounds like gas flowing. The Coast Guard has aircraft to collect SONAR from remote probes but it isn't charged with finding oil or gas reserves and would have no business fling over the North Pole.