When Mrs Butters opens the patio doors to ask her son if he has seen Eric, she closes the door after he says no but in the next shot the patio door is open again.
(at around 4 mins) An avalanche uproots the tree that is used as a landmark, but two shots later (at around 9 mins) the tree is shown standing. In the following shot, (at around 11 mins) the tree is shown broken and buried in the snow. Later (at around 24 mins) the tree is standing again. (at around 12 mins) the tree is standing once again when it should be gone.
The group of atheist sea otters are first identified as the "Allied Atheist Allegiance." But later (into part two), they're identified as the "Allied Atheist Alliance."
When Cartman is lying restlessly in bed watching the clock and waiting for the release of the Nintendo Wii, the clock reads 2:15 then 2:16. After a "while", Cartman looks at the clock for a third time and it reads 02:18. The zero wasn't there before. (Evidently this has been corrected in the version streaming on HBO Max.)