Continuity mistake: When Toad General calls for the council's attention and announces that Bowser found the Super Star, note his shirt buttons. Then, when he says that the Kongs will never agree because their mad king doesn't make alliances, Toad General's shirt is backwards, his buttons are on the opposite side. (00:24:55 - 00:25:35)
Continuity mistake: When Mario first consumes the Blue Mushroom, he emits a light that causes Donkey Kong to shield his eyes. However, later in the movie, when Peach forces Bowser to consume the same mushroom, no light is emitted. (00:49:15 - 01:21:22)
Continuity mistake: Near the beginning, Mario is picking something out of his plate and putting it on another plate. The scene cuts, and the plate has moved more towards Luigi.
Continuity mistake: When Peach and Toad return to the Mushroom Kingdom on her motorcycle, they enter through the back of the castle, across the lake, and then up a hill. Suddenly, they're both teleported to the very front of the kingdom (Toad village), as they drive back up to the Castle the way Mario did in the beginning.
Answer: "Princess Toadstool" was used in the original English-language manual, but she was Peach in the original Japanese, and that name continued in later versions, being combined with Toadstool. Bowser was originally called "Kuppa", but presumably the English-language version resonated more with people, plus removed any confusion of "Kuppa, King of the Koopas", so the English version stuck.