When SG-1 and Teal'c are fleeing the prison, Teal'c uses the word "Stargate" in place of "Chappa'ai."
When Daniel shows the others the Abydos cartouche containing the stargate addresses, Captain Carter states that she ran hundreds of combinations trying to make the Stargate work. Daniel says he tried the same thing. If Daniel tried any of the addresses, they should have worked as he was using a DHD which compensates for stellar drift.
It was mentioned twice that when a probe was sent to Abydos, it was flattened. The explanation given for this was that the gate had been buried. There are two problems with this. 1) If it had been truly buried, chevron 7 wouldn't have locked. 2) If it had been ineffectively buried, the vortex would have cleared enough room that the probe would have arrived intact.
In the pilot episodes #1.1 & 1.2, "Children of the Gods" Teal'c's supposedly permanent gold serpent marking is upside-down in a scene where he is talking with Jack. There are also some episodes where it is slightly crooked.
Daniel says each group of glyphs contains seven symbols, with each group being a Stargate address. But a Stargate address is only six symbols; the seventh is the point of origin, which changes depending on which gate one is dialing from.
The major who escorts Colonel O'Neill to the lower levels of NORAD is also wearing sergeant's stripes on the sleeves of his dress uniform. This does not appear to be a new character (same man who picked up O'Neill at his home) and you can see that he is clearly wearing officer's rank on his shoulder epaulets. Enlisted airmen wear nothing on their epaulets.
During her initial appearance, Sam stated that she had "100 hours over enemy airspace during the Gulf War." Yet her ribbons don't include either of the authorized Kuwait Liberation Medals (Saudi and Kuwait). By the time frame of this episode, she would have been authorized to wear both.
While in BDUs, the rank insignia that the character "Major" Kawalsky appears to be wearing is two connected silver bars, which would make him a Captain. A Major would wear bronze oak leaves, which he is seen wearing while in his Class A uniform.
The character "Major" Samuels appears to be wearing silver oak leaves, which would make him a Lieutenant Colonel. A Major would wear bronze oak leaves.
The female soldier that is kidnapped in the pilot tells her captives that she is "a Sergeant in the US Airforce". The rank she is wearing when she is kidnapped though is actually that of a Senior Airman.
The scenes looking down at the descending lift are actually shots looking up at an ascending lift. There is a looping cable visibly defying gravity 'above' the lift
When Daniel bumps into the Dial Home Device the first time SG1 arrives on Chulak, it wobbles.
On Abydos, right before Daniel dials Earth, some of the symbols on the DHD are blinking.
When Col. O'Neill is traveling down the second elevator, the scene shown is actually of an elevator going up.
When the gate teams are ready to leave Chulak and three soldiers are on a ridge laying down cover fire, wires from a series of buried explosives are visible, giving the illusion of blows from Jaffa weapons fire landing nearby.
In the opening sequence, when the Jaffa leave, the Stargate closes and the view is looking down, and the walkway is clearly seen going through the Stargate opening. The walkway would have been destroyed when the gate opened.
General Hammond says they are sending a Mark 5 nuclear bomb through the Stargate. The Mark 5 was only in service from 1952 to 1963.
When Apophis, Teal'c and various other Jaffa travel through the gate to Earth, the wormhole closes, but when they leave with the female USAF officer the gate is open, even though they didn't enter the control room and wouldn't be able to use Earth's system anyway, because of the difference between Earth's computers and DHDs.
As the SG-2 team is waking up on Chulak, the airman incorrectly addresses Major Kawalsky as "Captain."