Through most of the episode Reese has a bandage on his right hand. In the court house while he talks to Finch, the bandage is on his left hand. Then it's back on his right for the rest of the episode.
The scene at Oyster Bay alternates between shots of bright sunny weather and shots filled with dark fog.
The lowest official Social Security Number starts with 001, but several of the SSN's on the list Finch shows to Reese start with 000.
(at around 11 mins) Reese says "NSA or FISA", referring to the government organization that could have recorded the wiretaps. FISA stands for Foreign Intelligence Surveillance Act and is not an entity with operational capabilities.
During the final court scene, it looks like an aide switches on a tape recorder and cranks up the volume. The device however is a small two-channel club mixer with no recording or playback function, and the switch the aide flips is a channel input selector that doesn't serve any purpose in this context.
While at her office in Midtown, shown near the Empire State Building, Diane Hanson is told to meet her goons in Canarsie (far East End of Brooklyn) in 20 minutes - a typical 45-minute trip, more likely 1 hour in mid-day traffic.
Reese would not have let his fingerprints be taken, as it's ingrained into operatives to avoid that even in a poor state of mind. Also, his prints would never be found at a 'crime scene', because when working their prints have been removed and they wear gloves. Nothing is ever left behind.