When the crates are stacked on the boat, Melman's crate is big enough for him to move around in. However, when Alex is trying to help him out of it, it is obviously smaller, and Melman cannot even get out of it.
The animals take a subway from Central Park to Grand Central Terminal. They are seen on a subway platform on 59th Street and Lexington Avenue, which is the correct subway station that you would take from the south end of east Central Park. However, on the platform, the sign shows that that platform is for the 4, 5, and 6 trains. In reality, the 4 and 5 trains are express trains, and stop at express platforms underneath both the local platforms and a platform for the BMT Broadway Line. So except for during service disruptions, the 4, 5 and 6 would not all stop at the same platform (though late at night, 4 trains run local and use the local platforms). Also, the train is shown to be one of R62 stock cars. However, this stock has two sets of doors on each side of the car. In reality, IRT rolling stock has three doors on each side.
When Skipper asks the talking monkey if he can read, he says that he can't read but Phil can. Earlier on in the film, the talking monkey takes what appears to be a newspaper from a trash can and starts reading it. However, if you look at the newspaper, it is actually a comic.
Real lemur tribes have a matriarchal structure and not a patriarchal one. The female lemurs are the ones who lead the tribes and do most of the fighting. Instead of King Julien it should be Queen Julianna. However, his right hand man did say he was the self-proclaimed king of the lemurs, so he likely rules in name only.
The orientation of the word 'GIRAFFE' on Melman's crate changes when he uses it for a tombstone. (From parallel to the arrow to perpendicular). However, if you look closely earlier in the movie, you can see in certain shots, that the other side of the crate has 'GIRAFFE' perpendicular.
The crates are stacked on the deck with Gloria's crate at the bottom. The crates all appear to be of the same depth, and when seen from outside they appear to be stacked neatly, but there's still light coming into Gloria's crate from the hole in the top even though the hole should be covered by one of the crates stacked on top of hers. However, this was so that we would be able to see Gloria in her crate and not be staring at darkness (the same would have applied otherwise to Melman's crate as it was upside down.)
When on the ship, the penguins peep out of their crate through circular holes that are clearly big enough to let them out, especially for Kowalksi and Rico. There was no need for Rico to break them open with a fake key.