Protect Her - S1-E1
Factual error: When Jules and Hannah are talking about the financial shenanigans at Owen's firm, Jules says that the owner of Owen's company had fraudulently driven up the price of the stock before the IPO. This is impossible. The IPO is the first time the shares become tradeable.
Thank You for Not Driving - S1-E3
Other mistake: The scene in which Tayo's wife gets into her car to leave their home is filled with mistakes. First off, it seems to take her much too long for the short driveway to reach the curb. Then, when she is blocked by the perp's van, she rams one of the perps twice and then backs away. As she is backing away, the perp's body flies forward, smashing into the van. She then rams the van twice with great force, and yet her car has minimal damage, only to the corner of the car.
Factual error: The Royal Navy sailors are shown with just 'HMS' on their cap tallies. This was only seen in the Second World War for security reasons. In peacetime, the tally bears the name of the ship or shore establishment to which the rating is assigned.
Other mistake: Agent Maddy is approaching the scene of a downtown explosion and fire. She has her FBI badge showing on her belt. As she approaches the police line she rummages in her jacket and looks down at where the badge is, but reaches into the adjacent pocket to pull out another badge in a wallet. Why not identify herself with the badge on her belt?
Factual error: There are two Marines posted at Marine 1, the Presidential helicopter. Their pants are ridiculously long and not the image of Marines with well-fitted uniforms. Their position of attention is wrong, with the hands clenched and placed on their thighs as opposed to being fixed at the sides. Worse, when they saluted with their right hands were above the service cap brim, instead of the fingertips touching the bottom of the brim.
Deliberate mistake: Identical twins Beverly and Elliot have the exact same beauty mark on their faces, roughly on the smile line directly across from the right nostril. Identical twins don't share features like that.