When Chen moved into her apartment, it was a one bedroom that she had gotten within the last few weeks before this episode, yet now her apartment is a 2 bedroom. This is seen when we first see the apartment before Chen moved in that there as a wall where the 2nd bedroom is.
The distance between Nolan and Henry and Olivia changes between cuts in the living room.
While having lunch, Nolan calls Armstrong "Lieutenant Armstrong", but Armstrong is still just a Detective.
After Opal calls Chen to tell her that Olivia has just purchased a handgun, Chen and Bradford race from the station to find Olivia. In California, while you can buy a handgun from a pawn shop if the shop has a Federal Firearms License, there is a 10-day waiting period before the customer can take the gun from the store.
No range master would ever allow an officer to enter a live fire range even if she is the only shooter.
The female in plain clothes with Nolan and Harper in the motel room at the drug sting, is in the end credits listed as "Detective". But she's not wearing an LAPD badge, but instead one typical of a Federal law enforcement agency, and so is her partner. In that case, she should have been listed as "Agent" or "Special Agent". Given it is a drug bust, it's likely she is DEA.
During the stakeout at the motel, Harper wears the Sony MDR-7506 headphones backwards, with the red R tag visible over her left ear.