Other mistake: The T-800 manufacturing facility cannot seem to decide just how the T-800's are assembled. When John, Kyle and Star jump through the hole and land amongst a load of T-800 skulls, all of the skulls have eyes that are lit up, and the lower jaws already attached. However, in the next shot when we see the T-800's being assembled on the production line, eyes are inserted separately and are not lit up, and the the lower jaws are only attached at that point, not before.
Factual error: The FN SCAR-L used by Barnes would not have existed because it was only in early development when Judgement Day took place in 2004 and as such would never have made it into production.
Suggested correction: The FN SCAR-L was already being produced by the time Judgment Day took place. And even if it wasn't, it's possible in the 14 years after Judgment Day, the resistance (or other survivors) was able to continue its production. Also, keep in mind that the 2004 in this timeline was a bit more advanced than the 2004 of our world (where early prototypes of hunter killers and other machines from the future were already being assembled). Because of this, the weapon could have been produced earlier.
