Character mistake: It is mentioned the previous solar flare was 15000 years ago, and Shepard says that the ancients were in the middle of a war with the wraiths, but as stated in previous episodes the war lasted 200 years and ended 10000 years ago. (00:31:30 - 00:38:10)
Visible crew/equipment: After taking the enzyme, Mckay is talking to himself as he dials the gate. When he goes to push the centre button, an arm moves on the opposite side of the DHD. (00:09:35)
Revealing mistake: When they are escaping in the beginning of the episode, watch Rodney dial. As he finishes, one of the DHD address panels pops out and falls off.
Factual error: Anytime a character fires a missile at an airborne target, it's invariably from an M136 antitank launcher. The M136 is designed to hit relatively slow moving ground vehicles and is useless against fast moving airborne targets. (This is because used M136 tubes can't be reloaded and are very cheap to use as props).
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.
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?
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.
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.
Continuity mistake: In the beginning when the crew is in the jumper, Ronan Dex has his hair tied back. When they land on the island and walk into the camp, his hair is down, and then they have to run back to the jumper when the prisoners start shooting at them. When they get back in the jumper, Ronan's hair is tied up again.
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: 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.
Plot hole: In early episodes, when Sheppard and his team are attempting to capture a Wraith, they ambush him and his soldiers with tasers. The taser just irritates the Wraith. Why don't they have Zat guns? (The real reason, of course, is that Wraith stunners will be introduced in 2 or 3 episodes.) But it makes no sense to not bring such a useful non-lethal weapon along into unknown territory.
Suggested correction: Production-wise, Zats are a part of SG-1 and Atlantis should have its own "look and feel." In universe, it's probable that the SGC doesn't have that many Zats (they can't make them so every own they have has to have been captured at some point) and therefore wouldn't want to send a load off on what was thought of as a one way trip when the Atlantis Expedition first left. Plus there would be no guarantee that the Expedition would find any way of recharging or maintaining them once they got where they were going.
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.
Factual error: When Sam breaks her leg, Dr. Keller discusses with McKay the possibility of internal bleeding, then returns to splint her leg and offer her some ibuprofen for pain. A doctor concerned about internal bleeding would never offer a patient ibuprofen, as it inhibits blood clotting.
Audio problem: McKay is talking to Sheppard about the differences between himself and Rod, and at one point says that maybe Rod screwed up and was chosen for "a one-way ticket to another universe", yet his lips form the word 'galaxy'.
Continuity mistake: In the scene where Michael is first introduced to his quarters, he goes to pick up a picture of his parents. In the first shot, the laptop next to the picture is closed, but in the next shot through the security camera, the laptop is wide open.
Revealing mistake: One of the dots used to "steady" the CG within a shot remains in the shot for a protracted period of time. Its a blue dot towards the bottom right of the screen. (00:17:55)
Continuity mistake: After returning from the Daedalus, McKay talks to Nola about how he had been a god to them the past years. In the shots filmed from his front, the standard radio headset is visible in his ear. In the shots from behind, it is gone.
Continuity mistake: When the Atlantis team finds out that the experiment has caused problems in another universe, McKay's sister says to Rodney, something like,"You said that the chances of connecting to another universe that was inhabited were astronomically small." It was in fact Carter that said that.
Continuity mistake: When the Wraith have taken over the Daedalus, Dr. Keller's hair changes from being wavy to being completely straight and back to wavy.