When Jake and the squad are trapped in Nakatomi Tower by the 'locked' door it is obvious that the doors deadbolt thumb-latch is on their side of the door. Meaning they could have opened that 'locked' door at any time.
The "Texas State Trooper" car does not have the correct paint or decals of the Texas Department of Public Safety.
In the pictures showing Captain McGintley, he is clearly wearing a Sergeant's badge instead of a Captain's badge.
Chief Aggerton is wearing mostly "fake" commendation bars that are not issued by the NYPD above his badge.
Captain Holt wears his Commendation breast bar above his World Trade Center Breast Bar. When the WTC bar is worn, it is worn above all other medals, but below the American Flag bar.
The 9-9 squad borrows clothing from Tommy, Becca, and Steve Boyle, who are all male, yet the shirt Rosa wears buttons like a woman's shirt.
Jake's hair is different in the flashback scene to the first episode where he and Holt are talking, because the scene never happened and it was filmed years later.
The quick cuts of scenes during the 99's hasty return to Brooklyn include a scene of Chicago (subbing for Baltimore) and one of Oakland (subbing for somewhere en route via Amtrak from Baltimore to New York).
Part of Amy's plan to get Holt to his meeting on time involves Kevin meeting the squad at the train station in New York with a fresh uniform, then the squad taking cabs to 1 Police Plaza. If Kevin was meeting them at the train station, he could have driven Holt to the meeting himself. There was no need for the entire squad to hire several cabs to drive them all there (while Kevin either went home or to work, as he was not present when the squad arrived at 1 Police Plaza).
During the cold open, Jake is not initially aware of the news that their former captain died due to entering late in preparation for his dance presentation. Charles was in the break room. There is no reason Charles would not have been pulled into the squad's meeting about Captain McGintley's death.