When Rodney is pleading his case with Sheppard outside his room, his intercom mic moves higher up his face and down again multiple times between shots.
McKay might have intended this as a ploy, but, while he implies that Harry K. Daghlian's fatal criticality accident took place before the completion of the Manhattan project, it actually occurred on August 21, 1945 - seven weeks after the first nuclear test ('Trinity') and roughly two weeks after the bombings of Hiroshima and Nagasaki.
Harry K. Daghlian, the first victim of a criticality accident, is an actual historical figure, but the time between the accident and his death was 25 days, not 30.
Once again, Dr Weir talks of 'a solar system' when technically it is a star system. OK, so she's a Poli Sci major, but still.
Rodney is shown cleaning dirt and dust off of a panel in the outpost, but the floors are completely clean.
Near the end, when Dr. Weir is yelling at Rodney about destroying three-quarters of a solar system and giving his ego a rest for one second, it is very obvious the audio is mismatched with the video. Dr. Weir and Rodney are barely speaking and their body language has no expression of anger or disappointment.
The debris of the Wraith ship in orbit would not still be there after 10,000 years. Its orbit would have decayed and it would have burned up in the atmosphere long ago.
It could have taken McKay years or even decades to get the power source working successfully, which makes the rush on everyone's part more than a little ridiculous. Instead of running tests remotely or even doing months of simulations on Earth, for some reason, relatively smart people decide to start up a device and hope for the best.
Despite it being obvious, neither Sheppard nor McKay decide to fly beyond the horizon to avoid the weapon systems fire. The curvature of the planet and the fact that weapon was firing beams of energy (which must travel in a straight line) would have protected them from it until they could achieve orbit.