When the women escape and prepare to "take care of business", we clearly see when Snow White rips off her sleeves that she has a heart shaped tattoo with "Dopey" written on it on her right shoulder. Later, when she summons the critters to attack the tree guards, her right shoulder is bare.
When Shrek and Artie are captured by Charming, and Shrek insults Artie to save his life, Artie leaves and, in a following shot, is seen walking away some distance from the castle. However, when Puss, Donkey and the other fairytale characters bump into him later, he is back by the castle gates.
The morning after they meet Merlin, just before they are attacked by the Villains, Donkey can be seen with his legs sleeping on his back on the 2 first shot, then then camera change and when you see him again he is on his side still sleeping. The camera change is so fast that it cannot be attributed to he moving his position but to an error.
In the scene before the play sequence towards the end of the movie, the first shot is a wide shot showing the castle in the background with the path in front of it with Donkey, Puss, the Three Pigs, Pinocchio, Gingy and the Wolf just off to the right. The path is completely empty, and there is no sign of Artie in the shots of the path showing it behind the characters, yet seconds later, Artie suddenly appears on it.
When the boat crashes on the rocks, Shrek, Donkey, Puss and Artie end up on a beach. In all the wide shots before and after Artie walks away, there is clearly nothing on the ground around Shrek. Moments later, when Donkey tells him he should change his tactics, Shrek picks up a piece of wood on his left that wasn't there before.