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).
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.
Plot hole: Why do Dr. Beckett and Dr. Keller use so much Earth medicine? While the Ancients may have evolved past disease and genetic defects, they would still need treatments for physical injuries. And we know such advanced medical machines exist, scanners have been shown on screen and the Go'auld reverse-engineered their sarcophagi from an Ancient device. While they may be reluctant to use unknown machines for surgery or disease, surely bruises and broken bones should be healed instantly!
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)
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: At the end of 2-2, Runner, Weir shows Ronon images of the destruction of his home world - a fact he had been unaware of. But in "Trinity," Ronon says "all these years I thought I was the only survivor."