Continuity mistake: The pen used in the beginning of the drawing is different from the solid blue one used in the close up shot. Also, when the camera goes back to a wide shot, the color of the drawing on the whiteboard changes from blue to black. (00:17:40 - 00:18:35)
Continuity mistake: When Jackson is in the meeting about the symbols, he circles the seventh symbol with a blue marker. In the next shot, look close and you can see that the blue circle around the symbol is gone. (00:18:20)
Revealing mistake: When the crew is transported to the distant planet, there are three moons. They are all the same shot of our moon (the craters are the same), but each moon is turned differently than the other two. (00:33:15)
Visible crew/equipment: Throughout the movie, in the shots of the guys on the alien planet, the white reflector screens and film crew's reflections are visible in their sunglasses. (00:40:20)
Audio problem: Right after Jackson has been dragged through the desert by the creature, it wakes him up and he says, "Get away from me," but his mouth never moves. (00:40:30)
Continuity mistake: After the slave boy gets a cigarette from O'Neil, he reaches out to touch a gun, and O'Neil grabs it and scares the kid away. O'Neil is then holding the gun with the barrel pointing towards the door, but as the angle changes he is suddenly holding it at a different angle, pointing down to his right and away from the door. (01:05:30)
Revealing mistake: Right after O'Neil and Jackson are captured inside the pyramid and taken aboard the alien ship a distant shot is shown of the ship while it is opening. In the sky over the ship are depictions of three moons. Each of the three moons shown in the sky of the distant planet are actually the Earth's moon when it is full but just shown rotated slightly in different positions. (01:38:00)
Revealing mistake: In the scene where O'Neil is fighting Ra's bodyguard, the bodyguard uses claws and hits O'Neil's back, tearing his shirt and wounding him. But you can see Kurt's "wounds" and torn shirt right before he's hit by the bodyguard (a scene after Ra's bodyguard's claws are shown). (01:49:10)
Other mistake: When the ship lands atop the pyramid and begins to retract and open the topmost sections of the pyramid retract into the lower parts however the upper parts are too long to fit into them. In the next sequence we see the ship and the upper parts are nowhere to be seen.
Continuity mistake: There is no necklace on Catherine's neck when she greets Jackson in the room with the cover stones (00:13:39). After they have shaken their hands, the necklace appears on her neck suddenly. Then it disappears again. Also, after Catherine has given the necklace to Jackson for bringing him luck before his departure, the necklace appears on her neck again when she is in the control room during their departure.
Continuity mistake: When the men are in the pit of water the man who says "Colonel it's us", his dog-tags change from on his chest to back several times between shots.
Factual error: When they first power-up the Stargate in the military facility (using Jackson's decryption), the thing surges to life, and electrical sparks spray out of overloaded connections all around the control room. This could only happen if there were no fuses or electrical breakers in the military's control system, which is a ridiculous notion for such advanced military technology. In real life, a powerful overload situation would instantly burn out fuses and trip breakers and the whole system would simply go dead (there would be no sparks). Showers of sparks are a common error in many science fiction and space fantasy films dating back many decades.