When Charles is chasing the criminal down the fire escape near the end, his gun & holster falls off his belt, and is shown on the ground when the angle changes. However, when Jake comes around the corner and tackles the criminal the gun is nowhere to be seen.
When Holt and Jake are talking after Jake returns from the stakeout, his arms go from by his sides to folded repeatedly between shots.
The award that Raymond, Jake, and Rosa receive is not a police award. It appears to be a US Air Force Good Conduct Medal attached to a long blue ribbon. The Air Force Good Conduct Medal is awarded to enlisted Airmen for three consecutive years of good conduct in active service. It is not awarded to civilian police officers.
Jake is wearing 2 "fake" commendation bars that are not issued by the NYPD.
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. Also, most of the commendation bars 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.
Charles suggests calling a woman who arrives at the drop house "Mrs. Peacock" before adding: "Male peacocks are the colorful dressers." However, he does not need to specify that he is speaking about a "male peacock", since "peacock" only refers to a male peafowl. A female peafowl is called a "peahen".
Jake refers to seeing Holt smile as being similar to seeing a turtle out of its shell. The shell is part of the turtle's body, not a separate entity it lives inside, and is connected via tissue, blood vessels, muscles, etc. Removing a turtle from its shell would be akin to seeing a person with their rib cage torn off.