Continuity mistake: When Ted's mother comes to Alaska to find Ted, Ted is out looking for Jack. Ted's mother is standing at the finish line waiting for Ted. When we first see her she is holding a Teddy Bear, the shot cuts to Barb coming out the door than back to Ted's Mom and the Bear is gone.
Continuity mistake: When Cuba is driving in the Beetle with the skunk, the skunk is in the back walking around on the platform under the back window, but we cut to Cuba with a clear shot of the back window, and there is no skunk. Yes, Cuba's head is in the way a little, but that is a big, bushy skunk. Plus in the next shot they show the skunk again, and it wasn't in the place where Cuba's head would've been hiding it.
Continuity mistake: After Ted has rescued Jack from the cave, Jack is strapped to the sled and Ted is on the back, with both Nana and Demon as the 'lead dogs' (Jack's dogs are also attached to the sled, but this is irrelevant). In one shot, Nana is on one side, Demon on the other, but in the very next, their positions are flipped around. The ganglines make it impossible for the dogs to do this (cross over) whether they are stationary or moving, so it could not be that Nana merely decided to run on Demon's other side, or vice versa. And even if this was possible, you can see perfectly well that the lines are uncrossed and untangled; totally fine.
Visible crew/equipment: When Ted slides across the ice and it starts to crack, he moves from ice block to ice block until he is standing on one piece (and he tries to make his 911 call). The camera angle then changes to a top down view of him sinking. From this angle you can see the hydraulic table platform used to create the illusion of him slowly sinking, perfectly balanced on the block of ice.
Revealing mistake: When Ted arrives in Alaska he has to take a small, single engine plane to his destination. When he gets out of the plane, the runway is supposed to be covered with ice, making Ted seemingly slip, slide, and appear to be running in place trying to keep his balance. But if you look closely, you can see that he is wearing roller blades instead of boots when he is running in place.