Lucy was played by Liliana Mumy, who is the daughter of Bill Mumy who was in the 1960s TV show "Lost In Space." In the kid-friendly commentary, this is referred to but not directly stated; the filmmakers merely remark on the resemblance. See more...
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Factual error: When Santa is shown the miniscule print on the 'Santa Clause' card (that he is supposed to be/get married) the Elf holds an enormous lens in front of it, to make it easier for Santa to read the print. From the distance Santa is standing at, from his point of view the card should appear upside down.