The Three Blind Mice are turned into horses to pull the coach after the wedding reception, yet they are seen moments later dancing on the organ keys. A closer look reveals that there was a passage of time (perhaps a day) between these two shots.
Lord Farquaad summons the Mirror to show him a princess he can marry (to become King of Duloc). The Mirror presents him with Cinderella, who is not a princess in her own right, so Lord Farquaad could not become King by marrying her. Of the choices named by the Mirror, only Snow White and Fiona are princesses.
As Shrek and Donkey are leaving we see them walk through sunflowers before the onions and cabbages. Later as they are walking back, the sunflowers are farther away from the castle than any other plant.
When Fiona finishes off the rest of Robin Hood's Merry Men, she cries out a few seconds later that an arrow is stuck in Shrek's butt. However, if one looks in the few shots beforehand, there is none there.
When Lord Farquaad finds Shrek, Donkey and Fiona after Donkey discovers Fiona's secret, he gives Shrek a scroll, claiming it's the deed to the swamp. Later, when he leaves with Fiona, the scroll is nowhere to be seen.
When Shrek and donkey arrive at Duloc, Shrek scares the parking valet who then proceeds to run back and forth through the roped queuing area. When seen from above, he has 4 more rows to run, but when seen from behind, once he runs those four rows, he still has two more rows to run.
Near the end of the movie, when Shrek and Donkey are rushing to make the wedding, Shrek climbs up the chain to get on Dragon. Previously, it has been assumed that Dragon then flies off, but if you look closely, Dragon lifts Donkey onto her back with her paw, and Donkey is present at all times.
As far as we know, Fiona has spent her entire life alone in the tower, so she should have no knowledge of the outside world. Yet as her encounters with the songbird and Robin Hood demonstrate, she is more than capable of taking care of herself. However, it is revealed in Shrek 2 (2004) that she's spent at least a few years of her life outside the tower (from Fiona's diary), which might be the time when she learned her skills. Another theory is that she could have been practicing in her room in the tower.
Shrek makes jokes about Lord Farquaad's height even though he just learned of Farquaad's existence, and never saw him anywhere before except on a balcony. However, Donkey could have heard about Farquaad's height before, and told Shrek about it during their quest.
When donkey first meets Shrek, when Shrek confronts the knights, the shadows of the all people in the scene do not fall the same way, Shrek's shadow is casting more forward onto the leader knight, whereas the knight's shadows are off to their left.