Character mistake: When Daniel Jackson learns about the fact that his wife, Sha're, has returned with a dormant Gua'uld, he does not take her to Thor's Hammer that got repaired in S2E6. Even though he was with Teal'c, that doesn't pose any issues since he is deliberately exempted from the Hammer.
Touchstone - S2-E14
Character mistake: The team are finding out who could have stolen the weather device from Madrona and find an energy spike at the same time SG2 are on a mission. "But SG2's mission is galaxies away from Madrona" Says Teal'c. At this time the only missions the teams could go on was in our own galaxy and couldn't be galaxies away.
Character mistake: When Hammond and Carter come out of the base, Hammond is told he's been gone 22 hours. Hammond says he's only been gone about 20 minutes. To which Carter says, due to time dilation, time is moving an average of 600% slower and that telling O'Neill to wait 5 minutes would be 6 hours or more. However, 600% is just another way of saying "6 times" and time is slower by about 66 times, so she should have said an average of 6,000%. 5 minutes being 6 hours would be 72 times slower.
Chosen answer: Report 30185 is a joke report referring to the time when SG-1 go back in time to 1969 in the episode '1969'. The joke is that Colonel O'Neil knocked up a hippie and made sure Mitchel was taken care of throughout his life, like how he got into the 302 program while his buddy, a better pilot, did not.