The professor refers to the markings on the plaque as 'hieroglyphics'. An archaeologist studying Egypt would know that they are 'hieroglyphs'. 'Hieroglyphic' is the adjective used to describe the script and not the language.
Alexander wouldn't have been so consumed with Egyptian mythology as the show claims. He had been tutored since he was a child by Aristotle, and was not a superstitious person.
The ancient symbols on the parchment are arranged to allow for some of the tears in the paper, with blank spots near where the tears are.
The three pieces of the plaque barely hold together when it's assembled for the first time, yet the plaque is obviously just one solid piece in later views.
Steam is immediately produced after Mac adds the water after lighting the fire. This indicates that the container for the water was hot to begin with, which would be impossible if the tomb was only being opened for the first time.
None of the purportedly ancient artifacts show any sign of aging, which includes an impossibly legible and flexible ancient papyrus scroll.
After von Leer takes the eye, he laughs maniacally, but his lips don't move.
The tomb of Alexander has been hidden for centuries, but still has a giant window, in he shape of the Eye of Osiris, which lets sunlight into the tomb.
Professor Axford pronounces the Egyptian God Ra as "ray," instead of the correct way as "rah", and MacGyver then repeats the mistake.
At the end everyone acts like the tomb is now inaccessible because of all of the wreckage, but they have seemed to have forgotten that the Eye of Osiris was apparently a window into the tomb, which should make it fairly easy to reenter the tomb.