Audio problem: When Mario and Luigi are in the cave, walking along the cliff, Mario shouts "Watch out" but his mouth never moves. (00:21:25)
Audio problem: When Mario and Luigi are escaping the police station, after they see the Bob-omb, Mario says, "Goombas! C'mon! Let's go!" and Luigi says, "Look, it was trying to give us that thing!" Their mouth movements don't quite match what they're saying. (Granted, they're facing away from camera for most of the shot, but when their mouths are on camera, you can tell they're not saying that.)
Audio problem: When the officer asks "How many Marios are there between the two of you?" watch closely. In the wide shot for the second half of his line, his mouth is not moving at all.
Audio problem: When Koopa and Lena are introduced, there's a long wide shot of them descending some stairs while Koopa is talking about their master plan. ("I'll be able to merge our world with theirs and get rid of the mammals!", etc.) However, Koopa's mouth blatantly isn't moving at all for most of what he says. He just has an evil grin on his face.
Audio problem: When Luigi jumps through the portal, as Mario screams "Luigi!", his mouth is not moving at all.
Audio problem: When Iggy and Spike start to follow Mario's truck, they accidentally crash their car. As they drive away, you hear Spike say "Out of my way!" but if you look in the windshield, his mouth isn't moving.
Audio problem: Throughout the scene, where Mario and Luigi are driving to the plumbing job at the beginning of the film, there are multiple moments where their lips and dialogue don't match. It's primarily in the wideshots outside of their van.