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.
The chain around Dragon's neck is not there when Donkey summons her before the wedding scene, but it appears seconds later when Shrek gives Donkey a noogie. The chain disappears again after Shrek uses it to climb on to her.
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 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.
When Fiona, Shrek and Donkey camp the first time, you see Fiona eavesdropping from the cave after the sun has set. She wanted to camp for the night to avoid being seen as an ogre, but when the camera zooms in on her face, she is human.
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 first paints the "Beware Ogre" sign at the beginning, the top left corner is missing from the piece of wood. In the next shot, the top right corner is missing (as if the painting was done on the other side of the wood).
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.
There is a spigot on the barrel next to the one that Shrek whacks with the beer mug at the tournament, as seen in the overhead shot. Seconds later, when Donkey uses the same barrel to crush the knights, the spigot has disappeared.
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 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.
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.
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.
Farquaad does not seem to know where the fairy tale creatures are when he tortures the gingerbread man for information but he mutters 'indeed' when he hears Shrek telling him he dumped the fairy tale creatures on his property which could imply Farquaad did know where the fairy tale creatures were.
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.
The goof item below may give away important plot points.
Incorrectly regarded as goofs
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.