Character mistake: Tom Mason makes references to smaller armies defeating larger ones, of which history is rife with examples. He cites the Scottish defeating 'the British' at the Battle of Stirling Bridge. 'The British' did not exist at that time. The Scots administered a beating against the English in the Scottish War of Independence, against the Earl of Surrey, under Edward I. Someone with his level of knowledge would know that.
Eight Hours - S1-E10
Character mistake: Pope tells Tom that the weapon he gives him is standard Army issue except it has a mech metal warhead. However the weapon he gives him is an RPG-7, a Soviet designed and built weapon.
Character mistake: Deni tells Anne she got a report from a scout 1,800 klicks west from here. She might have meant 18, but 1,800 doesn't seem logical. A klick is 1 kilometer (or 0.6 miles). It's unlikely a scout is over 1,110 miles away, which would put him in the middle of Texas.