When Rebecca has Neal at gunpoint at the fortress, in the shots from over her shoulder, we see the gun against Neal's temple, level with his eyes. In the shots over Neal's left shoulder the gun is pointed at the top of his head and his left eye is visible.
When Rebecca calls Neal to tell him where to meet, the cell reception is just fine. When Burke asks for the Ranger's phone, he says there is no reception down there.
Mozzie told Neal he would be broke if he didn't continue as a criminal. He obviously forgot the treasure stolen from the U-Boat, which was worth more than either of them could spend in a lifetime. Plus Neal had many talents apart from being a criminal.
Neal said it was 5 years since he'd seen Paris. He was in prison at that time.
When Peter and Neil are at the campus, he says 33° is this way but he moves to the left 33° on a compass would be to the right so he would've walked in front of Neil not opposite Neil.