Plot hole: Huge plot error: Apophis and Clorell (Skara) should not have survived the explosion in Season 2, Episode 1 (when they attack Earth with two ships). In "Family" they explain that Apophis and Clorell survived by escaping through the stargate aboard Clorell's ship moments after Daniel Jackson did the same. However, when Daniel Jackson escapes through it, Apophis and Clorell are not even on the right ship, and there is 1 second left on the C4 timer when Daniel escapes. They actually show Daniel Jackson escape, and then cut to Apophis and Clorell still aboard their ship. So apparently, Apophis was able to "ring" from his ship over to Clorell's ship, make it to the stargate room, dial an address, and escape through the stargate all within literally 1 second. Is this guy related to The Flash?
Plot hole: When the team manage to create the cavern with the buried stargate they send Teal'c through to drill his way out, but wouldn't it be safer (and significantly faster) to fire a missile or two through and blast their way out? They have no idea how deep the stargate is buried, or under what type of rock, so sending Teal'c with only four hours of air seems suicidal. (00:35:00)
Character mistake: At the end, Vala and Mitchell establish a wormhole and let Teal'c and Jackson know. Almost a minute passes before Teal'c and Jackson get back to the gate and Jackson yells "run" because they need to get through the gate right away. Obviously they're detained, but after being let go, Mitchell says they're sending the iris code now. This is something that should have been done sooner, especially after hearing gunfire, so they could be ready to go through when Teal'c and Jackson arrived.
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.
Plot hole: The team go through the gate to disable a drone with the intention of being able to close the active Stargate, but once they go through in a submarine, the gate closes behind them, rendering the mission pointless. (00:24:18)
Factual error: At the end of the episode General O'Neill is introduced to Joe's wife. He is introduced as General O'Neill, but his insignia on his dress blue uniform is a Colonel - an eagle, not a General's star.
Stupidity: Some ancient advanced civilization took to the task of building this amazing net of stargates that enables instantaneous traveling over hundreds of light years or more, but any stargate can be disabled by anybody just by covering it with dirt or rocks. Apparently if the stargate is buried then it becomes inactive. See Season 1 EP.1.