In the first movie, Evelyn is a clumsy and shy librarian, whereas by the time of the second movie, she has become a confident warrior and a master of swords and guns. While some may find this a jarring change, if we consider what she's been through, along with her choice of husband and lifestyle, it's a very believable change for the ten year gap between movies.
She even mentions that Rick taught her a few good defensive moves. Plus there's the aspect of Mama Bear towards Alex, and the awakening of her former-life training as Nefetiri, an Egyptian princes trained in combat.
One of the deleted scenes in the first movie involves a pair of zombie priests digging out the Book of Amun-Ra before Rick and Jonathan can get to it, wherein they're sprayed with the same acid that killed the group who unearthed the Book of the Dead. Why delete the scene? Because no doubt the Egyptians would not have wanted to make it as hard to kill the creature as it would have been to release him.
Although the director did say that he cut that scene for pacing purposes.
Imohtep believed Evy looked like Anck-su-namun in the first movie because the eyes he took were from a man who wore glasses. Additionally, take into account Imohtep's reaction when he and Evy first meet in the first film - him peering at her in a manner implying he's trying to make out her appearance, and the questioning tone when he says Anck-su-namun's name.
Why did the Medjai never get cold feet, open Imhotep's sarcophagus and destroy him in a manner that he couldn't return from? Because they converted to Islam, which specifically forbids disturbing the dead (even a monster such as Imhotep) as haram.
Beni saved the world, this is not an exaggeration. I just realized after re-watching the trilogy. If you listen closely near the beginning of the second movie, you'll hear Jonathan say that the Spear of Osiris (the same spear needed to kill the Scorpion King) was a part of the loot that Beni packed onto the camels that he and the others rode off into the sunset with. Now think about that, had Beni not found that particular item and loaded it onto that camel, the whole world would have been subjugated by the Scorpion King and his army. Twisted but true, Beni's greed was the one crucial element to saving the planet.
When the mummy of Anck-su-namun wakes up on the table near the end of the first film, there's a neat little effect where we can see the table through the holes of her eyes and mouth... Except we should see the back of her head, since her skull is intact and she has wraps and the remains of hair.
Why Evy lost her glasses in the first film: either they were completely superfluous, reading glasses, or she lost them along with all of the other supplies when the boat sank. Also would explain (if they were, in fact, reading glasses, as the film suggests) why it took her so long to translate the inscriptions of where the Book of Amun-Ra was and the inscribing required to make Imhotep mortal.
What exactly were those pillars Alex knocked over in the sequel holding up?
They were just decorative.
In the first movie, Pharaoh Seti's "crown jewel" city was Thebes. However, in the prequel part of the second movie which took place a thousand years earlier, The Scorpion King (or his look-a-like grandson), destroyed Thebes using the Army of Anubis. Then, when Rick and Evie are at Thebes, the same fallen pillars are on the ground, unmoved for 5,000 years. Shouldn't have Seti have had the place cleaned up, since it was his capital city?
Possibly they were left to lie there in Seti's day, as a dreadful warning not to go anywhere near the Scorpion King's tomb?