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."
In the scene where Scott is trying to overtake the sleigh being flown by the plastic Santa, the plastic Santa says "You are a sad, strange man." This very line was used by Tim Allen in his voice role as Buzz Lightyear in Pixar's Toy Story.