When Rumpelstiltskin is threatening the witches, the amount of water in his goblet changes irregularly between shots.
When Shrek is crying in the woods, the tear is shown falling down his right side. However, when Donkey notices, he is standing to Shrek's left, from which angle the tear is not visible.
Shrek covers his escape from the castle by dragging a ball that's much too large for the window -- most of it ends up stuck inside the castle. As he flies away, most of the ball is visible on the outside of the castle. Cut back to the interior, and most of the ball is inside again.
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 witches are seen flying past him, 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.
The second film starts off with Prince Charming arriving at the 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.
When Shrek and Donkey escape Rumple's castle, Shrek grabs onto the chain from Rumple's pretty ball. Before he exits the castle through a window, he drops the chain and is seen pulling another one as he exits the castle. The aerial shot that is seen just after Shrek and Donkey exit the castle shows the chain with a much longer length than what Shrek pulled previously.
After Shrek punches the birthday cake out of anger, no one is covered in frosting. Given how massive Shrek is and the large force that was used to punch the cake, this should have happened, implying a direct violation of physics.
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.
Fiona complains to Shrek that the outhouse is clogged up. Medieval restrooms were either built of stone or were garderobes often incorporated into castle walls which were discharged into moats, that created a cesspool, not outhouses.
When Shrek first arrives at Far Far Away after being captured, the 24-hour timer only displays about 1-2 hours gone, but the journey, as shown in the second film, would have taken some days.
In the first film, it takes Shrek several days to get to the dragon's keep, but in this film when he has only one day before he disappears, he is able to get there in one day.
Because Shrek was able to get his life back, he would have never met all the other Ogres, yet all of them are present, as if old friends, at the end of the film.
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.
In the original movie, Shrek wanted to have friends because he didn't want to be alone. But in this movie, he wanted to be alone because he thought that he wasn't a real ogre anymore.
Shrek had several opportunities to present Fiona with the contract that he had signed with Rumpelstiltskin in order to get her to believe him.
As Shrek had seen notes asking for the capture of Fiona in the swamp, he should have known that she would no longer be locked up in the tower.
Both Shrek and Rumple incorrectly quote Fiona's curse as: "By day one way, by night another." The correct wording, as stated by Fiona herself is: "By night one way, by day another."
Donkey (and Rumple in the film's soundtrack) refers to Gingy as a cracker. Gingerbread men are either biscuits or cookies, not crackers.
After Donkey panics and screams that he has to save Shrek, Gretched pulls him back by his tail and remarks, "Don't be a fool, mule." The donkey is the father of a mule, according to natural selection classification.
When Rumplestiltskin is addressing the citizens of Far Far Away via the Magic Mirror, he says that whomever brings him the 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.