After Shrek visits the swamp and finds it dry, he is looking at Rumpel's contract while the witches are flying by. He has the contract on his right hand in one take, and after the witch is seen, the contract magically disappears.
Shrek picks up Fiona's handkerchief near the monogrammed corner, pulling it toward him. In the next shot, the handkerchief is sitting in the palm of his hand with the monogrammed corner facing away from him.
When Rumpelstiltskin is addressing the citizens of Far Far Away via the Magic Mirror, he says "whomever brings me this ogre shall receive the deal of a lifetime." It should be "whoever", because that is the subject of the sentence. "Whomever" would be referencing the object of the sentence.
After Shrek and Fiona share true love's kiss, evoking his contract's escape clause, he is returned to the original timeline having just given a roar at his children's birthday party. This occurrence had nothing to do with Rumpelstiltskin; had the terms of the contract truly been reversed, Shrek should have been returned to the moment he signed it, or when he first met Rumpel rather than any point beforehand.
The goof items below may give away important plot points.
Incorrectly regarded as goofs
Shrek 2 starts off with Prince Charming arriving at Dragon's Keep days after Shrek and Donkey unchained the Dragon and departed with Fiona. In the parallel universe, if Shrek and Donkey hadn't "rescued" Fiona, Prince Charming might have attempted to do so, but very likely would have been fatally burned by the still-present Dragon.