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)
Continuity mistake: When Tom Keen returns from shopping to find someone over the cot of baby Agnus, a fight breaks out, during which the camera jumps to different shots of the baby who is wrapped in a pink blanket, then no blanket, then back to wrapped in the blanket. (00:37:22 - 00:37:58)
Character mistake: After the seaplane crash lands off the coast of Havana, Elizabeth radios a mayday. However, she broadcasts nonsensical coordinates. The first set she provides is 23°52' north, the second set 82°49' south. These combined coordinates can't possibly plot to any location on earth. The more probable coordinates should've been 23°52' north, 82°49' west. These coordinates would put the plane roughly 57 miles NNW of Havana, Cuba. (00:05:48)
Revealing mistake: When turning the guy with C4 around his neck, the 4 person safe box window shakes briefly. If this was a bomb proof safe box, the glass would be at least 1.5"+ in thickness and would not shake simply from some walking. That box would be shrapnel to a C4 bomb inside. (00:26:30)
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.
Factual error: When Red goes to meet Zamani at the Lincoln memorial, he initially walks down the monument steps eastward, towards the reflecting pool in the direction of the Washington Monument and finds Zamani at the base of the steps. The map that is shown of his supposed location in front of the Lincoln Memorial when the FBI starts tracking him, isn't a map of the National Mall, nor the Lincoln Memorial. Later, when they are walking and he is "on the move, heading westbound", they are actually walking away from the Washington Monument, towards the Lincoln memorial, to the location where they had originally met (and discussed the Cherry Blossoms). Two seconds later, they are near 14th St, which is easily a 25 minute walk from the Lincoln Memorial. (00:33:25)