Other mistake: When Thor reveals to SG-1 that the Replicators have reversed the time dilation device, he says time is moving at a factor of "10 squared" (100 times faster than real time). Carter says that in the hour that passed, 4 days have passed for the Replicators (which is correct), but then says depending on when they did it, hundreds of years could have passed. But that's not possible since that means years in real time would have passed. But the Asgard didn't set this trap years ago, just recently.
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.
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)
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: When half of SG-1 return to Medrona to detonate a charge aimed at the gate, why didn't they just go to another planet? As when they went to Medrona, there was a blizzard going on and they also had the natives saying they will arrest them as they still hadn't returned the Touchstone. Could have just saved themeselves some hassle.
Continuity mistake: In the scene where SG-1 tries to get their note through the gate, watch Daniel. The camera cuts to him just before Jack slides down the zip line, and you can see small dots on Daniel's face - presumably the marks left when shot by the security system. However, Daniel has been taking cover since the alarms sounded and only gets hit when he tries to get to the gate after Jack is brought down. The next time Daniel appears on camera, his face is clear again and stays that way till the point in the scene where he, too, is killed by the security system.
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.)
Plot hole: The NID guys escape because Jack can't kill them. He fires his MP-5 around them to try to make them stop. Is there a reason he didn't bring a Zat gun along? The whole point of this mission was to stop the NID rogue agents without killing them and to capture them if possible. The Zat gun seems tailor-made for a mission like this.
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.