Other mistake: As the surviving characters discuss the fate of Westeros, 2 plastic water bottles can be seen tucked behind the chairs they're sitting on.
Snow Falls - S1-E3
Visible crew/equipment: When the horse carriage is ambushed, just as Princess Abigail can be heard screaming "Please, help me", the camera pans downward and a horse wrangler wearing a blue baseball cap can be seen in the lower left hand corner, hiding behind one of the horses. (00:03:20)
Revealing mistake: The swords Jayden and Dekker use often bend when striking each other, revealing they are rubber blades and not metal.