When Fast Tony is talking to the animal about how he can help her lose a thousand pounds she clearly has ears that even flop around when she moves her head but when her mate walks into the shot to tell her she is "already as thin as a twig" her ears are completely gone.
At the beginning of the movie, Sid is standing at the top of the huge ice wall ready to jump down the waterfall. Sid starts counting "1,2.." and by the time he counts "2 and 4/1000" Manny and Diego reach near him. A few minutes later when the camera zooms out (showing that all the ice is melting), we see that there was no way any of the 3 animals could have climbed such a high mountain at all.
When Sid is tossed from the branches to the ground back at his camp, one of the young animals that watches him fall, a Macrauchenia (the trunked, long-necked animal), is gone in one shot, and then instantaneously appears on the other side of the screen.
In the first Ice Age film, there is some talk about the beginning of a new Ice Age, stating that the first film takes place at the beginning of an Ice Age. When Fast Tony starts talking about the end of the Ice Age in the beginning of this film, Manny gets defensive, and goes on to say that the Ice Age has been going on for over 1000 years. If this is the case, than these characters would have to had lived for over 1000 years.
When Scrat passes through the golden gates, he picks up two acorns. When he does this, you can see five acorns at the bottom of the screen. When he picks them up, there are no more acorns left and he's now holding six acorns. He should be holding seven.
When the group is about to set off together after they first meet, Manny calls Ellie by name, but the only time it was ever mentioned before that was when she and the possum brothers were talking privately. He should not have heard it.
Opossums have a lifespan of 2-4 years. In the scene where Ellie meets the opossum parent and two clinging offspring assumed to be Crash and Eddie, she is an infant. If our related mammals the elephants are any clue, Ellie could not have possibly reached adult maturity before age 18. Her opossum brothers should have been long gone.