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.)
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)
Children of the Gods (1) - S1-E1
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.
Children of the Gods (1) - S1-E1
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.
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.
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.
Children of the Gods (2) - S1-E2
Revealing mistake: When Daniel, Jack, and Sam first meet the robed Jaffa in the woods, you can see the camera light in Daniel's glasses.
Children of the Gods (2) - S1-E2
Revealing mistake: When Apophis' queen goes back into the female Jaffa, it is obvious that the film footage was just played in reverse.
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)
Other mistake: When O'Neill first goes to visit Teal'c in his cell the symbol of Apophis on Teal'c's head is upside down.
Emancipation - S1-E4
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.
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)
Cold Lazarus - S1-E7
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.
Brief Candle - S1-E9
Other mistake: Jack made it quite clear that he was 40 years old when talking to Kynthia, so if his birthday was in '52, that would put him at 45, instead of 40 years old.
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)
Revealing mistake: When Hathor turns Jack into her first new Jaffa, you can see the line between his chest and the prosthetic that gives him the Jaffa "pouch".
Revealing mistake: When Carter is looking up Hathor on the Internet, the address bar says that the web page is on the C drive of the computer rather than a web URL.
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)
Singularity - S1-E15
Plot hole: After Cassandra has her first "heart attack" you see her in her room. Why isn't there one of those heartbeat monitors in her room?
Visible crew/equipment: When Daniel is talking to Teal'c in the jail cell, you can see a camera light reflected in Daniel's glasses.
Chosen answer: Report 30185 is a joke report referring to the time when SG-1 go back in time to 1969 in the episode '1969'. The joke is that Colonel O'Neil knocked up a hippie and made sure Mitchel was taken care of throughout his life, like how he got into the 302 program while his buddy, a better pilot, did not.