Rising (1) - S1-E1
Continuity mistake: When they first arrive on Teyla's planet, the DHD is close to the gate. When the wraith attack, the DHD is much further from the gate.
Continuity mistake: Right at the end, after the entity has gone through the gate, we get an overhead shot of McKay lying on the ground in front of the gate. His legs are stretched out straight. In the next shot, one of his legs is bent. He's unconscious, so he shouldn't have moved.
Continuity mistake: When they finally get through the gate by blowing the rear hatch (which serves as the exit ramp when open), they arrive on the other end with the ramp closed.
Continuity mistake: Right at the beginning, the crew of the jumper only dials five symbols into the DHD before hitting the engage button.
Continuity mistake: In the scene where the Wraith attack on the Mainland, Sheppard is stunned and falls with his right hand on his gun near his hip, but when McKay and the other guy grab him, to pull him to the gate, both the gun and his right arm are above his head.
Audio problem: Teyla's audio sounds way more high pitched then normal, either dubbed or a post production mistake. (00:06:00)
Continuity mistake: Before Merell enters the cage to be fed on by the Wraith, his collar is open. Next shot when he enters the cage the collar is fully buttoned. (00:28:08)
Revealing mistake: Steve (Wraith)'s belly appears not to match the rest of the Wraith character's skin tone. Clearly, it is a human body rather than an alien. (00:31:36)
Plot hole: General Hammond is promoted to 3-star general and command of the SGC is given to General O'Neill before the Atlantis gang even left earth. Why is it, that none of them find it the least bit odd that a 2-star Hammond greeted their return instead of O'Neill?
Suggested correction: The dream-state induced by the aliens had some ability to stop them from questioning their reality. (One of them takes quite a while to realise that a friend they're partying with died years before they left for Atlantis). It's not infallible or entirely consistent, but it would theoretically explain this.
Other mistake: In Shepard's apartment, there is a fresh pineapple and other fruit in his kitchen. This despite him having been in Atlantis for several months. This later turns out to be an artificial reality, but that should've been a big hint.
The Eye (2) - S1-E11
Visible crew/equipment: In the beginning of the show (before the intro starts), when you look out the window you can actually see two people shaking the small trees in the storm... Come to think of it, why would there be trees in the first place? How could they survive out there if Atlantis submerged in the ocean? (00:02:21)
Revealing mistake: When the team lands on the Planet and first step out of the Puddle Jumper, you can see multiple footprints going in and out of the puddle jumper from previous takes.
Audio problem: In the scene in the hallway when Sheppard and Teyla are dressed in hazmat suits and talking to Dr Weir via the intercom, you can see a reflection in Teyla's helmet of Sheppard's mouth moving, but there's no sound. (00:23:45)
Plot hole: After Zelenka is finished with his description of how Atlantis rose from the ocean, Ford asks him if he said anything that would require security clearance to see. But if he is worried about security, why did he film Zelenka sitting in front of a top-secret Naquadah generator? This would be the equivalent of a soldier filming Enrico Fermi (speaking in Italian) in front of a nuclear bomb prototype then asking if he said anything secret.
Visible crew/equipment: When Novak is talking with Caldwell on the comms about beaming a nuke inside the ship, you can see an arm in Hermiod's "butt" moving with Hermiod. (00:08:30)
