Executive Meddling: The original script had Daniel and Miranda getting remarried, but Williams, Sally Field, and Columbus (all divorcees) felt that they didn't want to give children of divorced parents an unrealistic ending.
Fake American: Lydia Hillard, the eldest daughter, is played by Canadian-born Lisa Jakub.
Fake Brit: invoked Daniel when in his Mrs. Doubtfire status.
Which is Lampshaded by not-really Brit Pierce Brosnan (his character is, while Brosnan is Irish, but he moved to London when he was ten) when he first meets Mrs. Doubtfire. He immediately spots that "her" accent is a bit muddled. Mrs. Doubtfire Handwaves this by claiming to have moved around a lot.
A super-obscure one: One of the men in the sound booth during the opening scene is voice actor Terry McGovern, who is best known as LaunchpadMcQuack, fictional commentator Peter O'Keefe for Sega's NFL2K franchise, and the voice for the befuddled Stormtrooper during the iconic "These are not the droids you looking for" scene in A New Hope.
Another rather obscure one: Scott Beach, better known as Mayor Grundy in Stand by Me and Mr. Gordon in American Graffiti plays the judge. This was one of his final roles.
Miranda Hillard is Mrs. Lincoln from, well, Lincoln.
Playing Against Type: In-universe example - Daniel, the happy-go-lucky life of the party, has to play a strict, crotchety old disciplinarian.
Technology Marches On: The film's plot would be completely rendered moot today as caller ID would have outed Daniel as the person calling for all the nannies applying, and people don't usually pick up for unlisted numbers anymore.
It likely would have required writing in Daniel searching around for still-functioning payphones, calling from different lines at work, borrowing friends and coworkers' cellphones, etc. So the plot would still work, it would just require a bit more footwork on the character's part.
Throw It In: Attempted within the movie, and it doesn't go well.
What Could Have Been: As mentioned in Executive Meddling above, original plans had Daniel and Miranda remarrying. In addition the original script had Stu being a more snide character, ready to ship the children off to boarding school.
A sequel was planned, but then Robin Williams died.