Santa (Art Carney) wears a hearing aid in his left ear
The front of Santa's sleigh says "Clement Sea". Immediately after we see this, Santa talks about how 'Twas the Night Before Christmas is his favorite poem and that he named his reindeer based on Clement C Moore's famous poem.
When Santa (Art Carney) tries to prove to Claudia that he's Santa, he knows that she was living in Houston, Texas at an early age. In real-life, Jaclyn Smith (Claudia) was born in Houston, Texas.
Scott Grimes (David) also appeared in the Christmas TV Movie "It Came Upon the Midnight Clear", which also aired in 1984.
In this film, Paul Le Mat is married to "Charlie's Angels" star Jaclyn Smith. In "The Burning Bed", which also aired on TV in 1984, he was married to "Angels" star Farrah Fawcett.