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: Peach's crown suddenly appears on her head a few cuts after taking her helmet off.
Continuity mistake: During the kart ride to Cranky Kong's castle, a wide shot of the kingdom is shown, showing only two ramps on either side of the entrance. However, moments later, there is now a third ramp in the middle, leading to the entrance. (00:42:42)
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.