There But For the Grace of God - S1-E20
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: When the Jacks are talking to each other right at the end, the camera goes back and forth from looking over each of their shoulders at the other one. If you look closely, the false Jack's earlobe structure changes when we see him from behind.
Continuity mistake: When the sarcophagus explodes, the blast door they escape through has no card reader. Once they stand up it's there. (00:37:55)
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)
Children of the Gods (1) - S1-E1
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: When Omoc is approached in the infirmary, he takes off the oxygen mask. But in some shots, the mask is just pulled down and still around his neck.
There But For the Grace of God - S1-E20
Continuity mistake: When the Goa'uld attack the alternate Earth they dial in so no-one can escape. However in future episodes the Russian Stargate program said that as long as a DHD was hooked up to their gate it would have priority. When the invasion happened they had a gate on the ship hooked to a DHD.
Suggested correction: The Goa'uld are well aware of this. All they would need to do is block the event horizon of their Stargate or disconnect the DHD and any incoming wormhole would default to the gate on Earth instead.
Children of the Gods (1) - S1-E1
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)