Character mistake: Sometimes in the show, when a Goa'uld or Tok'ra is speaking (as opposed to the host speaking), they will say "my symbiote", such as when facing danger or illness: "my symbiote will protect me" or "my symbiote will heal me." However the Goa'uld and Tok'ra are the symbiote and they should be referring to themselves protecting or healing the host's body.
Factual error: Before SG-1 switched to P90 PDW's, they carried MP5 submachine guns. They were often shown with a full magazine taped upside down to the one in the weapon, so that to reload, all they have to do is remove the magazine, turn it over and insert the full one. Team members were also shown doing just that in several fight scenes. Problem is, real special ops troops are specifically taught in training never to do this. It's far too easy to damage the lips on the spare magazine, rendering it useless. There are clips that will hold magazines upright side by side, but its easy to see on screen they weren't using them.
Plot hole: Anytime an SG member starts acting weird or something happens that is "impossible", SGC personnel always act skeptical about it. Considering what they have seen in the course of the show, "that's impossible" should have long ago fallen out of their vocabulary. And while I realize that Sam and Daniel are scientists, they have seen enough examples of incredibly advanced technology that they should be far more open-minded when looking for explanations.
Other mistake: In several episodes throughout the series, SG-1 is coming through a planet's Stargate but there's no sign of a MALP, even when it should be in the shot. SGC wouldn't send a team through without sending a MALP first (not only to check for a DHD, but survey the land, check for habitability, etc). And if the idea is "well, maybe they have a recovery unit go fetch it before SG-1 goes through", then why would the MALP be present in all the other episodes?
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.)
Continuity mistake: As the female soldier approaches the gate when its first activated, an alien device is thrown through. You can see in the shot that the device will land much further away from her foot than what is shown when the shot changes. (00:02:25)
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: 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.
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)
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.
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.