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.
Suggested correction: While the other correction lists a 59th street, that's in Brooklyn. There is one in Manhattan though, 59th - Columbus Circle, which is also the south-west corner of Central Park.
Suggested correction: There is definitely a 59th street subway station: https://en.wikipedia.org/wiki/59th_Street_ (BMT_Fourth_Avenue_Line).
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.
Other 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.
Suggested correction: When we see the outsides of the box on the ship we can also see little gaps caused by wood planks nailed to the sides of the box so there should be a little light coming from in between to Gloria's box holes.