When Colonel O'Neil returns to Abydos, to retrieve Dr. Jackson, the first Abydonian boy who jumps around a corner with a M4A1, has no magazine in the guns receiver, and when the camera changes to a front view of same boy there is a magazine in the gun.
Captain Carter says that the planet they're going back to is (one of) the closest to Earth, which is why they can still access it using the old "address" even after millenia of stellar drift/expansion. But in the original Stargate movie, it's described as being "somewhere in the Kalium Galaxy," on "the other side of the known universe."
When Colonel O'Neill is escorted into the SGC at the start of the film in the elevator he is escorted by someone who is in USAF Uniform but wearing both Major Pins (Officer) on his shoulders and Staff Sergeant Chevrons (Enlisted) on his upper arms.
The credits name Jay Acovone's character as "Captain" Kawalsky, when in fact, it's "Major" Kawalsky.
Arriving outside the SGC, the arriving car's left tires roll over a marking reading "CAUTION - NO STEP", indicating that the surface lacks the support underneath for human weight, so a car's weight should be right out.