When Detective Carter walks in to save Finch she's completely dry, even though she's supposed to have come in through torrential rain.
There doesn't seem to be an 'Owen Island' in NY. According to 'The Machine', they are on 'Shelter Island'.
When the fisherman is dragging Reese towards the water and Reese regains consciousness, Reese grabs an oar. Reese's feet are bound together. In the camera switch, Reese is instantly on his feet swinging the oar horizontally at the fisherman's head. Reese could not have possibly gotten up instantly, let alone with his feet bound with the fisherman holding the rope to his bound feet.
When Bear is barking and clawing at the door to the incinerator in Rollins' basement, the hand of the animal trainer (presumably) can be seen pointing to the incinerator at the far left-hand side of the screen.