Continuity mistake: After Toad is turned into a Goomba, when Koopa is talking about his own evolution, Toad goes from being shackled to the chair to be unshackled and leaning forward instantly between cuts.
Continuity mistake: When Koopa is explaining the devo chamber to Mario and Luigi, we see a monitor showing an x-ray of Toad's de-evolution. When the camera cuts from the wide shot to the closeup, the monitor has suddenly gone back in the animation and replays the same segment again.
Continuity mistake: When Mario and Luigi are giving their names to the officer, at one point, another officer breaks a glass and we see shards of it landing on the book in front of the officer. A few shots later, most of it has vanished.
Continuity mistake: When Mario and Luigi are giving their names to the officer, there's a woman randomly rubbing her foot against his arm and shoulder throughout the scene. However, the way her foot is on him changes multiple times throughout the scene.
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.
Revealing mistake: When the old lady falls into the car, she blatantly turns into a dummy for a few shots. (She literally doesn't move at all and is unnaturally stiff.)
Continuity mistake: When Big Bertha picks up the old lady, she goes from holding her in front of her to holding her above her head instantly between cuts.
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.
Revealing mistake: When Mario and Luigi first arrive in "Dinohattan" and fall through the railing, you briefly get a clear look at Luigi's stunt-double, who appears to be a bulkier man who looks nothing like John Leguizamo. It goes by quick, so it can be hard to see, but once you notice, it's obvious.
Visible crew/equipment: When Luigi and Mario are chasing after Iggy, Spike and Daisy, during the shot where Mario is talking about "breaking every bone in their body," watch the shadow at the bottom right of the screen. At one point, you can see movement in the shadow from a crew member that got caught in the light.
Audio problem: When Luigi jumps through the portal, as Mario screams "Luigi!", his mouth is not moving at all.
Continuity mistake: When Mario and Luigi are in the cave, Mario goes from Luigi's side to behind, to being on the other side between cuts. There's no point in time where either they (or their feet) aren't on camera, so it makes no sense.
Continuity mistake: When Daisy and Luigi are looking at the fossils, after Luigi says "You're beautiful," the distance between him and Daisy increases instantly as it cuts to a wide shot.
Continuity mistake: When Daisy is showing Luigi the fossils, as the camera cuts from the wide shot to the closeup (when Daisy says "Have a look!"), suddenly their heads go from facing up to facing down between cuts, as do their flashlights.
Revealing mistake: When Daisy takes Luigi to the dig site, there's a long wide shot as they talk and start to head down. As the camera zooms in, you can see the composited background (the bridge, city, etc.) "jiggle" slightly towards the end of the shot where the composite effect didn't quite align up.
Continuity mistake: When Iggy and Spike round the corner and snatch Mario's girlfriend, the look on Iggy's face changes as it cuts from a close-up to a wide shot.
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.
Continuity mistake: When Mario is watching Luigi trying to talk to Daisy after she gets off the phone, he is tapping the empty water bottle against his head. In the first shot, it's against his forehead, but in the next shot, it's suddenly down by his cheek.
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.
Revealing mistake: In the opening, when Daisy's mother pushes the beam and causes the cave-in in the mine, for a split second, you get a pretty clear shot of Koopa's stunt double, who is taller than and looks nothing like Dennis Hopper. He's only on-screen for about a half-second, but it's very easy to notice it.