When Goodnight is sitting in the cafe, the condiments are at the side of the table, then later they're in the center, then back to the side.
In the first sequence in the tavern we can read the neon BBQ sign the correct way from the inside of the room, making it read backwards from the street. In the last scenes there, the sign is hung correctly so that it reads backwards from inside, and the right way from the street.
Secondary police employment must be approved by the NYPD. The NYPD patrol guide procedure 205-40 prohibits members from working for someone with a criminal record. As such, Danny could never have worked for Goodnight.
The female officer says after the public argument she had with the male officer that the patrol guide does not cover this, speaking about her relationship with her partner. In fact the NYPD patrol guide does regulate officer's conduct while on duty and in uniform. Any conduct such as the argument and battery (face slap) would be a violation.