Other mistake: After arresting the Reddington impostor, Ressler states that while hunting Red they had only one photo with a "passing resemblance to the man we've been working with." In S1E1 you can however see a high quality picture of Red on the front desk screen while he is arrested. (00:32:25)
Other mistake: Elizabeth picks up a stuffed bunny which supposedly was from her childhood. The bunny has burns on it after being in a fire. You can see 2 plastic tag fasteners attached to the bunny, which wouldn't have survived the fire.
Other mistake: It shows an eagle-eye view of the downed plane with the pontoons floating separate from the plane; the plane starts to sink more and Agent Keen incorrectly says that one of the pontoons is taking on more water, even though they aren't attached to the plane and keeping it afloat anymore. (00:05:55)
Other mistake: When Reddington is close to death and is saved by a lung/heart operation in his field hospital, minutes after the operation the site is attacked and Red is left trying to defend himself from gunmen. Not only does he find the strength to pull out all the monitor wires and lines attached to him, but when he goes into the corridor to get a gun, he is fully dressed in jacket and trousers (pants). Did the very efficient hospital team forget to bring a hospital gown for him to wear? Did they operate on him while he was wearing his street clothes?