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Fan Nickname: "K. Ron" (after L. Ron Hubbard) for Kristy and "BSCult" have become popular on some snark communities.
Name's the Same: Two characters are named Sabrina Bouvier - a child beauty queen that BSC meets in Little Miss Stoneybrook ... and Dawn, and later a classmate at SMS.
Lampshaded in Here Come the Bridesmaids! where the narrator acknowledges that both the BSC and the W♥KC have a regular sitting charge named Ryan DeWitt, and no, they're not related.
Technology Marches On: A big deal is always made of Claudia having her own phone line for them to use as the Babysitters Club number. Nowadays they'd probably all have cell phones.
What Could Have Been: A planned spin-off would have been called Morbidda Destiny, Teenage Witch, based on Karen's belief that her elderly neighbor Mrs. Porter was a witch whose real name was Morbidda Destiny; but the idea didn't do well with test groups and was scrapped.