Humiliation Conga: Pete and his henchmen. Firstly the real prince shows up just as Mickey is about to be crowned, outing Pete as a treasonous would-be usurper, then a battle ensues where Pete and his whole freaking guard get their butts handed to them by Mickey, Donald, GoofyandPluto, as well as the Prince. Pete tries to pull an I Surrender, Suckers move on the Prince, but only with short-lived success. And if that wasn't humiliating enough, Pete endures an incredibly embarrassing moment in front of the whole court and exits by being caught up in a chandelier and crashing through a stained glass window, his frilly underwear still on show.
I Surrender, Suckers: Pete tries to do this to the Prince during the climactic Sword Fight. He admits defeat and asks the Prince spare him, after which Pete bows down before him, saying, "Your Majesty is too kind...". But the Prince (and not Pete) is standing on a rug, which Pete then pulls out under the Prince's feet, and the battle resumes.
Intermission: Not in the movie proper, but in the film's theatrical release with The Rescuers Down Under, a 10 minute intermission started during this film's end credits to allow people to get up and take care of business before The Rescuers Down Under started, as shown here.
King Incognito: In this version, The Prince is smart enough to take along his royal ring as identification when necessary.
Private Tutor: The prince is introduced receiving instruction on Trigonometry from the chamberlain, who seems to handle the prince's education as well, and bored out of his mind. The prince begins to amuse himself by tormenting Donald Duck.
Rodents of Unusual Size: Played straight with Mickey (as usual) and the prince, but averted with a female peasant mouse that shows up for a few seconds of one scene.