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.
Revealing mistake: The swords Jayden and Dekker use often bend when striking each other, revealing they are rubber blades and not metal.
Revealing mistake: When the students see themselves in the TV, (which meant that Skidmore was watching them because Chyna had given her a hidden camera) you can see in the TV that there is actually a green screen on the screen and the video is not actually playing, it was just edited in later.
Dan Vs. the Animal Shelter - S1-E5
Continuity mistake: When Dan is pulling the meatloaf out of the oven, Chris knocks. You see the chain is attached from the door to the wall. In the next shot, the chain is undone without Dan having done anything.
Episode #1.4 - S1-E4
Other mistake: Dr Ambrose, talking about a doctor tending to patients on death row, says "Hippocrates is spinning in his grave." The subtitles say "Hypocrites is spinning in his grave."
Continuity mistake: When Irina meets XIII on the river dock, she leaves her car, closes the driver side door and walks to XIII. Moments later, when XIII is shot, she runs back to her car, where the door is wide open.