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 onto 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 Donkey passes out (after the arrow incident), some dry leaves can be seen drifting up from the floor. However, in the next, wider shot there are no leaves to be seen.
Disappearing shield on the wall behind Shrek at the tournament. It is there when Shrek is announced as champion, but then is gone in the next shot.
When Shrek uses the outhouse there is a toilet flushing sound. Outhouses use no water.
During the wrestling scene, Donkey yells to Shrek to 'tag' him but no 'tag' is made, normally in a tag team match the legal participant (wrestler in the ring) tags his tag team partner by slapping their hand (or body). Shrek does not slap Donkey's hooves, what happens instead is a 'double team' where Shrek has the knight in a full nelson and Donkey headbutts the knight. Also, Shrek continues to wrestle in the 'ring' anyway so a 'tag' weren't have made sense even if it had been made.
The three blind mice and the woman who lived in a shoe seen in Shrek's swamp are not actually fairy tale characters but nursery rhyme characters.
As the dragon chases Shrek, Fiona and Donkey while they try to escape the castle, the chain attached to its neck 'flows' at the same speed as the dragon. But when Shrek locks it with a sword, by plunging the blade through links, the chain is static. And it then takes ages for the slack to be taken up, just as the dragon approaches the footbridge. The chain would have been tight from the start of the chase, with no slack.
"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."
Cinderella is one of the earliest Disney princesses, although not a princess by definition. This is a deliberate choice of the filmmakers, who are satirising fairy tales but Disney in particular. For example, Farquaad's character has been recognised as a jab at Michael Eisner, the CEO of the Disney Corporation when Shrek was filmed.
As far as it is known, 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 her 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.
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 looked at closely, Dragon lifts Donkey onto her back with her paw, and Donkey is present at all times.
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.
Geppetto and Peter Pan are seen selling Pinocchio and Tinker Bell but given they are also fairy tale beings they should have been arrested and rounded up as well. However, only fairy tale creatures are being rounded up. Geppetto is merely an ordinary man, and if he walks instead of flying, Peter Pan will pass as an ordinary boy.
During the campfire scene, with the shot that has Shrek looking at the camera, his left eye goes through the left eyelids.
When Donkey first meets Shrek while Shrek confronts the knights, the shadows of all people in the scene do not fall the same way, Shrek's shadow is casting more forward onto the leader knight, whereas the knights' shadows are off to their left.
When Fiona, Shrek and Donkey camp the first time, Fiona is seen 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.
Shrek uses an outhouse. As this film is set during Medieval times, 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.
After Fiona knocks out the Merry Men, Shrek, obviously impressed, comments, "Now hold the phone", a meaningless phrase given the time period of the movie.
The sun sets in different directions with respect to the same view of Lord Farquaad's castle.
In order for Fiona to break the curse she was under, she had to receive a kiss from her true love, which was why she believed she had to marry Lord Farquaad. However, since Farquaad was not her true love, kissing him would not have broken the spell regardless.
When Shrek rushes to the wedding he tells Fiona that Lord Farquaad just wants to marry her to become king, but given the fact that he was not told this there's no way he could have known about it to tell her.
Farquaad does not seem to know where the fairy tale creatures are when he tortures Gingerbread Man for information, but he mutters 'indeed' when Shrek accuses him of dumping the fairy tale creatures on his property, which implies that he knew all along and his interrogation was pointless, unless there were other fairy tale creatures that were still loose.
In this film it is implied Shrek lives alone because of his looks and the fact he is an ogre which frightens the villagers and this seems to upset him. However in Forever After it is the exact opposite where Shrek now wants to be feared again. It is possible Shrek simply got used to being feared by the villagers in this film and that his life was better living alone.
Lord Farquaad 'hires' Shrek and Donkey to go and rescue Fiona from her tower prison. But it should had been either impossible or very difficult to find the tower especially how it is implied the trio do not know where the tower is. Plus Shrek would need at least a map or compass to find the tower. It is possible though the magic mirror gave Farquaad directions or less likely Shrek and Donkey may have heard of the tower and have a rough idea where it is.
After Fiona has cooked the eggs, she asks Shrek how he likes his eggs. This is a pointless question, considering that she had already fried them.
Farquaad calls Fiona his wife at one point during the climax. She would had only been his wife had they been married which didn't happen. She was still technically his fiancee.
The Dragon's name is Elizabeth. However, she is never mentioned by name in the film. Her name was revealed in a set of Shrek figurines.
When Thelonious suggests "Pick number three, my Lord," to Farquaad, he is holding up two fingers instead of three, so it looks like he is asking him to pick Snow White instead of Fiona.