After Nick gets punched in the nose, in later scenes his wound suddenly heals with no sign of any injury.
Trains from New York to Boston leave out of Pennsylvania Station, not Grand Central.
In the morning, when Brooke and Nick return to Grand Central and get on the phone to call their "future selves" the public phone booth is identified as New York Telephone a NYNEX Co. NYNEX became part of Verizon in 2000. So, at the time of the movie in 2014 (14 years later), references to NYNEX were no longer around. Thus the phone booth would be labeled with the Verizon logo.
After Brooke has missed her train at the beginning, there is an announcement that, "Due to Port Authority security regulations, the station is now closing." However, she is at Grand Central Station, which is part of Metro-North. Metro-North and the Port Authority are two different agencies, with no regulatory overlap.
At 40:16, Brooke has no lip movement when she is talking on the phone. Her phone calls are montages of shots showing her speaking and emoting without speaking.
When Nick is playing his trumpet in the subway, the sound is that of a muted horn but the visual shows no mute in the trumpet.