Revealing mistake: When Alex says they should go find the penguins, he says "To home" and Marty, Melman, Gloria and Julien place their hands on top of his hand. In the next shot it shows all of them together. But due to the position of Julien and his arm length, it would have been impossible for Julien to have his arm fully placed on Alex's arm.
Other mistake: In the scene where Vitaly jumps the flaming hoop again, in the shot before he says to light the hoop on fire, if you look at the dogs you can see that three of them do not look like they do in the rest of the movie. One of them even looks completely different.
Continuity mistake: In the shot before Vitaly starts the new show, there are only five dogs when there should be six.
Factual error: After Captain Dubois escapes from jail, she looks up missing lion on a computer and finds a news page with Alex on saying "FAMOUS CENTRAL PARK ZOO LION MISSING" and hits the Print Screen button on the computer and the news page prints. However, pushing the Print Screen button wouldn't print a document. It would just take a copy of the screen. No matter how much you push the Print Screen button, the page wouldn't print off.
Audio problem: During the escape from Monte Carlo they all drive a van off a roof to land on the roof of the Hotel Ambassador. Captain DuBois drives her bike of the same roof to catch them. While she is in airborne she jumps off her bike onto the roof of the Hotel Ambassador and the bike falls to the ground. Yet we don't even hear the bike landing on the ground at no point despite the fall only taking a few moments.
Factual error: When Julien is about to pull the switch to turn the power off in the Monte Carlo casino, the sign above the switch says "LE POWER". Monte Carlo is in France so the sign should be in French. Obviously "THE" is in French as "LE". But "POWER" is not in French. The sign should have said "LE POUVOIR".