Anne Hathaway mentioned having a retainer when she was younger, that gave her trouble speaking. So Garry Marshall wrote the retainer scene in, and had Anne bring her old one.
It was also Anne's idea to be wearing a pore strip on her nose when Michael visits Mia at her house, and for the brush to break in her hair as she's getting her makeover.
Career Resurrection: Julie Andrews had dropped off the radar for a while, especially after a botched surgery left her without the use of her famous singing voice. The success of this put her back in the public eye, giving her film career a second wind. She enjoyed a new image - of a Cool Old Lady occasionally Adam Westing her more famous roles. Big roles in the Shrek and Despicable Me franchises followed.
Creator In-Joke: When Mia drops something at the state dinner, a waiter says "it happens all the time". The same actor played a waiter in Pretty Woman, also directed by Garry Marshall.
Dawson Casting: Just about. Anne Hathaway was eighteen playing a fifteen-year-old who turns sixteen. Heather Matarazzo was the same age, and Mandy Moore was sixteen.
Defictionalization: Of a sorts - Heather Matarazzo now runs a podcast called "Shut Up and Listen", like Lilly's show.
Franchise Killer: Julie Andrews said a third movie was planned, but the critical disappointment of the second put a halt to those plans. Anne Hathaway was also thought to be too old to reprise her role as Mia. A third film was again announced in 2016, but shelved once again upon Garry Marshall's death.
Missing Trailer Scene: The trailers for the sequel contained a reaction shot for Mia when Clarisse says "shut up!" in the courtroom ("Grandma said shut up?") that doesn't appear in the film.
When Mia accidentally sets fire to a man's arm at the state dinner, the flames were supposed to go out when he put his arm in the ice bucket. They didn't, Anne Hathaway panicked and threw water on him. The take is used in the final film.
When Mia and Lilly are talking on the basketball court, Mia slips and falls. That was Anne actually slipping then staying in character.
Late in the sequel, when Mia and Andrew kiss, we cut to a shot of a goat... One that moos like a cow. According to the audio commentary, this was accidental, but kept in because such a thing, in Julie Andrews' words, would be okay in Genovia.
The relationship between Joe and Queen Clarisse was a throw-in by mutual agreement between Julie Andrews and Hector Elizondo, who felt that a romance between people over 50 was important to tell. When the sequel came around, it became a major plot point.
During production, the filmmakers found that cutting to Charlotte for a reaction shot was a good way to end several scenes. So in the credits, she's billed as 'Charlotte Kutaway'.