In the rain scene, when Sid asks Manny "So what about you? You have family?", Manny turns away from Sid. The camera is on Sid in this duration, so we don't get to see Manny turning. The shelter is so small and snug, it should be impossible for a mammoth to turn around without first coming out.
After they jump the river of lava and Sid is trying to wake Manny, he audibly says, though it's muffled, "You're standing on my nose." When Sid asks him to repeat himself after he moves, it changes to, "You're standing on my trunk."
In the ice cave, Sid turns around a bend, looks right (heaves a sigh of relief), and then looks left to find the scary fish fossil. Then he turns right and immediately sees the dinosaur fossil. There was no dividing wall or corner between the 2 fossils, so the dinosaur should have been visible to Sid even before he saw the fish.
When Roshan is crying and they're trying to figure out why before the melon scene, Sid picks him up after the notion of BM is mentioned. When he says 'Why am I the poop checker?' he spreads his arms, and is no longer holding the baby. The camera wasn't on Manny long enough for Sid to put Roshan down.
In the first shot of the human camp, the camp is on the left side of the river that leads to the waterfall. During the tiger attack, the camp switches places to the right (note where the baby's mom jumps).
When the mother pushes the baby towards Manny, the baby is on a sloping rock and Manny pulls it towards him with his trunk. The next moment the baby is on the flat ground beyond the sloping rock. For that to happen, Manny should have either pulled the baby right off the edge of the slope to the ground with a thud or lifted and gently lowered it.
In the opening sequence Scrat is running along a valley floor when he is squashed between two colliding mountains of ice. When he is ejected from the crevasse, he is suddenly thousands of feet above the valley floor.
In the first camp-out scene with Diego, Diego is sleeping close to the rock wall when Sid returns. There is an overhead shot, and he is only a few feet away from Manny and Sid. Later, in another shot, just before he gets up, he is back by the wall.
After Sid, Manny, Diego and Roshan are trapped inside Diego's "shortcut" by the avalanche, Sid walks straight into a slab of ice at face height before falling down and getting his tongue stuck. When he gets up again a few seconds later, the slab of ice has disappeared.
When Scrat's coconut falls from the tree, it has already had its husk removed. (The directors confirm this on the DVD commentary. They may have been worried that a lot of their audience would not recognize a coconut with its husk on.)
The first animal to step on Scrat in the opening is a mammoth, yet no mammoth is visible in the long shot of the crowds of animals. In fact, no mammoth other than Manfred is seen throughout the sequence. With this, a large bird also steps on Scrat, but no birds are seen in the crowds. We also only see two legs of each animal stepping on Scrat even though three of them are quadrupeds.
Just before Sid comments that his "feet are sweating" there is an overhead shot of all three main characters walking along the snow. Their feet are moving but their bodies are moving forward far faster than their steps would take them and they appear to be sliding forward on the snow.
When the sabertooth pack is chasing Sid and he "skis" away, Sid is kicking up powder and leaving tracks in the snow, but during the early stages of the chase, his pursuers are running across the top of the snow leaving no tracks.
The goof items below may give away important plot points.
The baby accidentally slides down an ice tunnel, which appears to be roughly twice the size of the baby in diameter. The animals pursue by sliding down the same tunnel, which has somehow expanded to twice the size of the mammoth.
At the end of the movie, Scrat is seen frozen in ice. The ice is floating on the ocean with 90% above the water. The ice should be lower in the water with only a small fraction above the water line. Only a huge wave would then be able to wash Scrat onto the beach.