When Jake rips off the tape saying "hostage" to read "hos", the rip in following scenes is different than in the initial scene.
When Jake shoots one of the ATF agents with a paintball, the agent winces in pain. Jake shoots him in his bulletproof vest. The impact of a paintball would not be felt through a bulletproof vest, much less cause any pain to the wearer.
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.
Gina complains that she hates the ocean, saying, "That's where that stuck up bitch Rose let Leo die. There was plenty of room on that door," a reference to the film Titanic (1997). The issue in the climactic moments of Titanic was not that there wasn't enough room on the door, but that Jack's weight, in addition to Rose's, would have been too much for the door to stay afloat.
After the Nine nine squad capture the hostages Terry gets riled up and asks Charles for another 'Clip'. A police officer, especially a Sargent should know that a the correct term is magazine. As a 'clip' references a different loading device.