Continuity mistake: In the scene where SG-1 tries to get their note through the gate, watch Daniel. The camera cuts to him just before Jack slides down the zip line, and you can see small dots on Daniel's face - presumably the marks left when shot by the security system. However, Daniel has been taking cover since the alarms sounded and only gets hit when he tries to get to the gate after Jack is brought down. The next time Daniel appears on camera, his face is clear again and stays that way till the point in the scene where he, too, is killed by the security system.
Continuity mistake: When Teal'c walks into the Goa'uld force shield on the planet, he is forced off and he almost does a backflip. You can see that he would have hit the floor head/neck first. But when the shot changes, you see him land on the floor sliding on his back, as though someone had just pushing him over.
Revealing mistake: When Teal'c and O'Neill are passing by Jupiter (after the failed missile burn), you can see a reflection in the background window of the cockpit. But the reflection is not the backside of their helmets, but instead is the front sides matted on to give the minor illusion of a reflection. (00:19:20)
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)