Deliberate mistake: Bowser has several teeth that appear and disappear throughout the movie. The best example of this is when Mario is trying to grab the Power Star. We see Bowser snarl at Mario before he picks him up. There is a gap between his two front teeth. However, when the scene cuts from Mario's horrified face to Bowser's face, there are now extra teeth inside that gap.
Continuity mistake: When in the cyclone stadium scene, you can see two water people behind Gale. But later, a different water person is sitting next to the same water person on the right.