Children of the Gods (1) - S1-E1
Factual error: The escort for Colonel O'Neill is wearing both Major and Staff Sergeant rank insignia. Probably what the writers thought was a "Sergeant Major", which does not exist in the Air Force. Major is a commissioned officer, sergeants are non-commissioned officers.
Factual error: At the end when Ms. Finster tells Randall to give her the names of the kids involved with the ball incident, she says to list them in alphabetical order. The first name Randall says is "Dettweiler, T.J." But "Blumberg, Mikey" would actually come before that, and given what we know of Randall, this isn't the kind of mistake he is likely to make.
Factual error: When His Divine Shadow lays on the table to have his brain removed, the machine cuts his skull open and simply reaches in with a three pronged hand and tugs on the brain pulling it out. It would not have worked this way... The brain is about the same consistency as gravy and the prongs on the hand/claw putting pressure on it to pull would have caused them to sink into the brain's tissue destroying it. Also it pulls the brain out without cutting or separating it from the spinal column and merely just pulls it out from the top. This would have caused his brain to be torn into pieces as it was tried to be pulled off the spinal column, not come out perfectly in one piece as shown. (01:09:00)