Continuity mistake: When Daisy approaches Mario and Luigi after making a call at the phone booth, Mario goes from looking sideways at Luigi to looking down under his car's hood between cuts.
Continuity mistake: When Koopa is pushed into the chair in the Devo Chamber, suddenly a puddle of goop appears on the floor, and you can see that Koopa is sitting atop an empty uniform that wasn't there before. (There was a short, deleted scene where Koopa used the chamber to reduce a worker to primordial slime, leaving the puddle on the ground and the empty uniform on the chair. However, as the scene was cut, the puddle and uniform appear out of nowhere in the finished film.)
Continuity mistake: When Toad is talking to Mario and Luigi in the jail cell, he has his arms dangling down through the grate into their cell. When the camera is looking up at Toad, his arms are sticking through grates that don't align with each other, but during overhead shots his arms are through grates in the same row.