In the opening sequence of the first movie, the camera pans over an ancient Egyptian city that is identified as "Thebes, City of the Living."  The Great Sphinx and Pyramids are visible in the background.  Yet Thebes is hundreds of miles south of Giza, where those monuments are located!  Later, as they board the boat in Cairo, the pyramids are in the right place, in the background.   Also, in the second movie there is a scene of the bad guys' train going through Cairo, and the pyramids are in the right location.

Near the end of the second movie, Rick rushes to get Alex into the pyramid before sunrise.  He succeeds, the final battle between good and evil takes place and they escape in Izzy's balloon, and fly into the...sunset?  The battle only took an hour or two, tops!

Whose face appears in the plume of black dust/smoke that rises from the pyramid, after the Scorpion King is killed?  The only character known to make his face appear like that is Imhotep, but at that point he's lost his powers.  The Scorpion King, then?   That's what the novelization says, but why him?  I don't know, it just seems weird to me.  o_0

What happened to the Book of Amon-Ra in the second movie?  The novelization explains that Meela, knowing it was the only thing that could harm Imhotep, threw it into the pit full of scarabs at Hamunaptra.  That makes perfect sense to me, but if you haven't read the novelization and have only the movie to go on, that's a glaring plot hole.

In the flashback fight sequence in TMR, Seti pronounces Anck-su-Namun's name incorrectly.   He calls her "Anuck-soon-yamun" instead of "Anck-soo-namoon."  In my fics I poke fun at this, cutting on him for not saying it right.  Was that an intentional thing in the movie or did it just slip past the producers?  [EDIT:   I have been informed that Seti's pronunciation is actually the more accurate of the two, according to those who know about ancient Egyptian linguistics.  I stand corrected!]

I could be wrong, but I'm pretty sure they just made up that stuff about cats being the guardians of the underworld in the first movie.  Bast, a.k.a. Bastet, the cat-headed goddess, had nothing to do with death or the afterlife at all.  Her department was domestic life.

In TMR, just before the bad guys try to dump Evy in the fire, Meela snaps her fingers...with gloves on!    o_0

How did the three mercenaries in the second movie know the O'Connells had survived the flood, gotten the bracelet and were taking it to London?

When the dirigible crashes in Ahm Shere, Izzy makes a big fuss about how he'll never get it working again.  Yet by the end of the movie, he has.  This is never explained.   True, you can see he's set up some sort of fire to put hot air  in the balloon, but before he'd insisted that wouldn't work.

If the Curator didn't stick his arm in the wall until after Imhotep and Anck-su-Namun entered the pyramid, who lit all the torches?  Everything's lit up when they enter the chamber where Anubis steals his powers!  Did Imhotep light the torches with his powers?   If so, wouldn't they go out after he lost them?

In the first movie, as Evy is graphically describing how the ancient Egyptians mummified people,   she says they took out the heart, but this isn't historically true.  They left the heart in since that was what got weighed to gain passage to the afterlife.

Not exactly a blooper, but more of a continuity issue...  In the first movie, somewhere between the last scene in the streets of Cairo and the time he emerges from the sand vortex, Imhotep loses the black shirt he was wearing.  During the mob scenes in Cairo he has some sort of plain black garment underneath his trademark black robe.  When he's on the dunes outside of Hamunaptra, all he's got underneath that robe is a kilt.   Not that I'm complaining, mind you...  ;-)  A similar thing happens in the pyramid of the Scorpion King, in the second movie.  In the scene where Anubis steals his powers, Imhotep has a black robe on that covers nearly all his body.  Soon afterward, as Anck-su-Namun begs him not to face the Scorpion King, he's just in his kilt again.

Whose camels are at Hamunaptra at the end of the first movie?  Rick, Johnathan and Ardeth arrived in Winston's plane.  Imhotep, Beni and Evy arrived in the sand vortex.   Yet there's a herd of domesticated camels complete with saddles, etc, milling around outside the city.   Also, if there were so many there, why, (aside from romantic cuteness) did Rick and Evy double up on the camel on the way back to Cairo?   Granted, I wouldn't mind sitting in his lap and riding off into the sunset myself ;-) but it's not exactly practical.  I mean, Ardeth took one camel, Johnathan rode one, and Rick and Evy shared one.  There were many more camels than that wandering around.  Just an observation.  :-)