Continuity mistake: At the beginning of the movie, when Marty finds the snow-bullet in Alex's mouth, he puts it in the Alex thing collection, but the collection wasn't there before and it disappears after that.
Factual error: In the sequence where the animals get on the first subway, it says they are on the 59th St subway. But, there is no 59th St subway in NY. The only subway station close to 59 is the 57th St subway.
Other mistake: In the scene on the boat where the mute monkey is reading the notice on the penguin's box, and signing to the other, the monkey who can speak (but not read) is translating faster than the mute monkey is signing. For instance, he states the notice says "Kenya" before the mute monkey fingerspells "Kenya".
Continuity mistake: When Alex runs angrily after Marty on the beach, the footprints on the sand disappear faster than they should.
Continuity mistake: When Marty opens the thermometer from Melman, he puts it in his mouth and then spits it out, but it then disappears.
Continuity mistake: At the beginning of the second scene, you can see a man with a camera filming the penguins, but when one penguin says, "Smile and wave," the camera man has disappeared.
Continuity mistake: When Alex's crate gets knocked off the ship, there is water dripping into the crate, yet in the following shots the crate is completely dry.
Deliberate mistake: When Alex, Marty, Gloria and Melman are talking together inside the boxes, Alex has three holes in his box allowing light in for him. Melman, Marty and Gloria have that too, but Gloria's box is lying under Alex's and Marty's, so it can't get as much light - but it does.
Continuity mistake: When Alex tries to get Melman out, he is lying near the sea, but when Alex tries to get him out with the tree, he is farther away from the sea.
Other mistake: When the animals are on the ship being transported, the hippo's crate is below the lion and the zebra crate. The opening is below both the crates making it impossible for the light to be projected through the opening.