The fire extinguisher foam on Terry and Holt after they walk in on the Jimmy Jab games appears and disappears between shots.
There were no laptops in 1982. The laptops shown appear to be from the late 1990s.
Chief Fisker wears a captain's rank device when he should've been wearing an NYPD chief's rank device of four flag officer's stars.
Most of the commendation bars Deputy Chief Wuntch wears are not issued by the NYPD.
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.
Wuntch's commendation bars lack the black "WTC" commendation, given to all NYPD officers who served on or in the wake of the 9/11 attack on the World Trade Center. Holt, Terry, and most high-ranking officers seen throughout the series have it. Wuntch has served in the NYPD at least as long as Holt, so she should have received the WTC bar.
Jake douses the ceremonial bagel in alcohol before lighting it on fire, but only pours it on the left side of the bagel. When the bagel is lit, the top and center portions of the bagel ignite, not the portion that had been doused in an accelerant.
Amy continues to try forcing herself to eat the spoiled Chinese food even after Charles drops out. Because the Jimmy Jab games eliminate the loser from each round, once Charles dropped out, none of the others had any reason to continue eating. They would all advance.