When Lt. Ford is escaping in the puddle jumper, the blue light from the stargate appears (reflecting on his face), before the jumper has actually lowered into the control room. There would be no such light in the location where he dialed the gate.
The nuclear weapon which is detonated above the city's shields in order to mask the activation of the cloak produces a mushroom cloud. However, such a cloud with a huge stem is only produced when a ground burst detonation occurs, it is produced by dust and debris being flung up by the negative phase of the blast. The dust and debris are not present in the air above the city shield, so there should only be the 'top' of the mushroom, formed by the bomb's fission products.
Near the beginning, SGA is under vicious attack from wraith ships. This includes 1 hive, multiple cruisers & hundreds of darts. There are many dead SGA military and civilian personnel, including countless wounded. At this time, Dr. Beckett (head Doctor of emergency and all medical treatment) is standing in the headquarters of Atlantis. Obviously, Dr. Beckett should be conducting triage for all of the wounded casualties; a huge real-time mistake in the heat of a battle.
After the nuclear detonation over the city, McKay says "If we switch to cloak before the blast radius diminishes, we'll all be incinerated." However, the heat to incinerate is radiated from the fireball and has little to do with the blast (except causing it.) You want to keep the shield up after detonation to avoid blast damage, not heat damage.
When the Daedalus is deploying nukes for the second time against the 12 Hive ships, the radar shows a silhouette of a Prometheus-class at its center, not the new and very different Daedalus-class ship.
Boom from the nuclear explosion in space is heard at the same time as the first light is seen. There should not be a boom at all (space, remember?) but even if there were, it should arrive minutes later.
On the bridge of the Daedalus, the light used to simulate the impacts on the shields can clearly be seen on the glass panel with green grid lines.
When Dr Beckett comes to tell them that Ford has escaped you can see a yellow tape mark on the floor where Tori Higginson is standing.
Rodney points out the danger to the city that the blast-wave from the nuclear explosion would present if they lowered the shield too early, that the heat from it would incinerate Atlantis. However, he fails to take into account that the greatest threat to the city (more to the point, the city's inhabitants) once the shield is lowered would be the massive amount of radioactive fallout from the explosion. Without the protection of the shield, the city would be showered with lethal amounts of ionizing radiation.
Ford never possessed the ATA gene (nor did the Doctor's Gene therapy work on him), and thus has never been able to operate Ancient technology, like a Puddle Jumper. Also, he is seen operating it from the "passenger" seat of the Jumper, not in the driver seat.
When Sheppard is aboard the Daedalus, he is told that the Asgard wouldn't add weapons because they didn't want to give anyone weapons that might be turned back on them. Thor (when appearing before the committee in SG-1) stated that the Asgard were installing both shields and weapons on the Prometheus already.