Continuity mistake: Rick's wrist brace is missing in prison and during the trek across the desert, with no sign of the tattoo we learn in the next film is under it.
Visible crew/equipment: In the opening action-scene, as Rick backs away from the wall when the raiders start to leap over, there's a shot behind him where the camera pulls back... and you can see a near-perfect row of white markers (likely for the extras or actors) in the sand. There's at least five of them in a line.
Revealing mistake: In the first shot of the movie, the camera moves from the Sphinx through a town square. If you pay attention to the people in the crowd, it becomes painfully obvious which people are real (who were filmed in front of a green screen and composed into the scene) and which people are CGI. There's at least 4 (likely more) CGI people in the town square to populate it more, and they all noticeably move with a stiff, generic "walk-cycle" and even look slightly "blocky," like they're low-polygon models.
Visible crew/equipment: In the beginning of the film, when Ardeth Bay is first seen and talking about how "We, the Medjai, the descendants of pharaoh's bodyguards, kept watch," look closely. You can see the shadow of the camera move up Ardeth's horse's head as it closes in on him.
Plot hole: If the Medjai are supposed to be the guardians against Imhotep and sworn to make sure he never comes back to life then why weren't they in possession of the key that opened everything in the first place?
Suggested correction: Because it got lost in the centuries that passed. It's possible they don't even know every step on how the mummy can return.
Continuity mistake: During the foreign legion battle, the defensive line starts to retreat from the wall, falling under the force of the attack. Rick is at the centre of a group of five soldiers who are more or less in a V-pattern. When the camera changes position from front to back, there's just 3 of them.
Other mistake: At the hotel after the American has been relieved of his eyes and tongue and the motley crew realises the "waters" have turned to blood, Rick encounters Evelyn outside and behind her is a sign for "offices" that seems a bit too modern for the times.
Revealing mistake: When the boat with the Medjai is heading towards the ferry, you see the one attach the hook to his wrist. You can see the bulge of his fist at the end of his sleeve, where he attaches the hook. If he was really without a hand, it would only be as thick as his wrist.
Character mistake: Henderson asks the guy as he's leaving the room to get him some bourbon. They already drank in the bar and spat it out when they found out that everything had turned to blood, so it would still be blood.
Revealing mistake: When the scarab beetles surround Benni at the end of the film, watch closely... you can see many scarab beetles running directly "through" each other, revealing they are just a digital effect. (This is also visible in other scenes with the beetles, but it's most obvious in this scene, particularly in the first shot when the beetles begin to swarm towards Benni).
Continuity mistake: When everyone jumps off the burning river boat it is heading away from them, but in the next shot the boat is just starting to pass everyone while they are reaching the shore.
Factual error: In the scene where the Americans find the chest containing the canopic jars, the egyptologist reads the text from left to right. However, the text actually begins from the middle and goes to both directions: one sentence goes from right to left and the other from left to right (this was very common in Ancient Egypt as hieroglyphs could be written in both directions) So, as he started from the left, the highly trained egyptologist was actually reading the inscription backwards.
Continuity mistake: When Imhotep takes Benny as his servant, he holds out some gold items in a very skeletal hand (where he had the gold when he had no pockets is another matter). When O'Connell and friends are leaving Hamanoptera, Imhotep's hand comes out of the sand. You can see that it is either a prop hand, or a crewman's hand in a glove, as it is thicker than it was a few moments before.
Continuity mistake: At the stand off at the base of Anubis, when Beni says, "There are 4 of you and 15 of me. Your odds are no so good". O'Connell crosses his right arm over to point a gun at Beni, but they are no longer crossed immediately after when replies, "I've had worse."
Continuity mistake: When Evie shows Dr. Bey the ancient Egyptian map, she points at Hamunaptra with her left hand, but in the next shot, based on her body position, she's pointing at the map with her right hand.
Continuity mistake: In the scene where Imhotep's sarcophagus first falls through the ceiling Jonathon is practicing his golf swing a few feet away from Rick and Evie. When the sarcophagus falls exactly where Jonathon has been standing, Jonathon is suddenly 20 feet away without having had a chance to move.
Continuity mistake: In the scene where the group is waiting on Evie to decipher where the black book is, Jonathan runs out to get the car and it's pointing one way. When everyone runs out to get in the car, it's now pointing on the opposite direction. There's no way he could've turned the car around that fast.
Continuity mistake: When Imhotep's coffin is first found, O'Connell blows the sand out of the lock where the key is supposed to go. For the rest of the scene, the amount of leftover sand in the lock (particularly the arches) changes from shot to shot.