The German soldier identified as Gerhardt Wagner (pronounced in German as Vogner) in the historical footage is wearing an Army (Heer) uniform. As it is said Wagner served with U-boat command (Befehlshaber der U-Boote), he should be wearing a Navy (Kriegsmarine) uniform.
When Neal meets Sara at the archives, Neal brings her some food. Archives seldom allow ink pens, but they never allow food, not even if you're FBI.
At about the 25:42 mark, Peter walks around Mozzie and steals money from his pocket. As Peter is walking around the money can already be seen in Peter's hand.
The Lock on the Glass Door Burke is trying to pick is not connected to any locking system. Glass doors like this typically have a magnetic lock at the top of the door. Stanzier also enters a similar door on the opposite side of the room without issue during the blackout.
About 5 minutes into the episode, Peter talks with Neal over Diana's car's phone. During the scene the microphone equipment on his back is clearly visible.
During the heat wave in New York, Neal bumps into Sara who has just returned from Argentina a few days before. He asks how it was and she replies, "hot". When it is Summer in New York it is winter in Argentina. The weather there would have been about 50 degrees, not hot at all.
In the episode "Unfinished Business", when Neal is having lunch with Sara at the roof of the FBI building, Sara mentions that she was her parents' only child. However, in this episode, Sara tells Neal about her older sister who ran away when Sara was 13.
In this episode, there is a whole scene where Mozzie teaches Peter how to hide a bug and retrieve a bug from a target. The focus is for Peter to use his index and middle finger like tweezers and never put his thumb in the target's pocket. However, later when Peter retrieves the bug from Stanzler's pocket, he puts his whole hand in the pocket. This goes completely against what he just learned.
When Mozzie offers to make popcorn, Neil asks for butter. Mozzie has previously said he is terribly lactose intolerant. Later Mozzie is seen eating the popcorn.