Character mistake: At the beginning of the episode, O'Neill refers to the planet as P3X-989. When he awakes as an android, he says "Welcome to PX3-989." The P3X becomes PX3. (00:03:35)
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
Plot hole: When Apophis and his Jaffas are leaving SGC with the captive soldiers - there is no way they could have activated the gate without a DHD, but somehow it gets activated, and they escape.
Singularity - S1-E15
Revealing mistake: At the end of the opening credits, they approach a group of three dead bodies to tag them. The second body we see, wearing a light grey shirt, moves its head a little as they are passing the first body. (00:06:00)
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)
Revealing mistake: The shot of Daniel right after Conner says "They only come out at night," you can see the the breath of Daniel. The only time you see that is when It's fairly cool outside. The planet is suppose to be on the warm side. (00:08:30)