Plot hole: Before the last chevron locks & the wormhole engages, Carter asks "Where's the iris" to which Hammond responds "Someone used a remote, whoever it is has our codes". All well and good, except without the wormhole being active, they wouldn't be able to receive the code.
Factual error: Earth's Stargate is dialed up more then once in series 1. Mostly in the first episodes, the passive gate is also shown with a rotating dialer ring when being called. This is not correct. The called gate only illuminates the chevrons. (This is classed as a 'factual' mistake within the show, not a 'continuity' error, and the option to change type has been removed.)
Character mistake: After trading the pistol for Carter, Jack says "there's only 5 more rounds in that clip." However, the pistol didn't have a clip, it had a magazine, which is completely different. As a member of the Air Force who has been trained in firearms, he would know the difference.
Factual error: The escort for Colonel O'Neill is wearing both Major and Staff Sergeant rank insignia. Probably what the writers thought was a "Sergeant Major", which does not exist in the Air Force. Major is a commissioned officer, sergeants are non-commissioned officers.
Factual error: Carter claims that the gates shift position because of the expansion of the universe. Gravity sources within a galaxy completely compensate for such expansion. The gates would still experience "stellar drift", which is mentioned earlier in the same episode. Stellar drift occurs because stars orbit the galactic center independently.
Continuity mistake: When Daniel returns to the SGU in the alternate reality and Cathrine shows him the map of where the Goa'uld attacks on Earth are, we can see that there are no attacks in the north of Europe, but when we see a closeup Oslo, Stockholm and Helsinki have suddenly been added. (00:14:10)
Continuity mistake: During the surgery, when they attempt to remove the Goa'uld, they start a timer. The timer starts at 00:00:00, then it blacks out (obviously, you don't want to be bored by major neck-surgery), and then the timer is at 01:19:49. However, seconds later (after Carter and Daniel's conversation), look at the timer in the background, it reads 00:23:46. (00:32:35 - 00:33:10)
Continuity mistake: Kawalsky's rank changes. At the beginning of the episode, he wears the rank insignia of a Captain. However, when his is in dress blues for mission briefing he has on Major insignia. Then in the meeting after the Abydos, he's back to wearing Captain bars.