After Ritchie makes his sandwich and is explaining to Doug and Carrie that the cop will never show up in court, Ritchie's beer switches back and forth from being opened to closed and opened again.
Carrie brings Doug a Styrofoam container of leftovers from her date with Jeffrey. The camera changes angle and a metal spoon has now materialized out of nowhere as Doug begins to eat the leftovers.
When Doug, Spence, and Richie are helping Carrie select an outfit for the date, the blinds between the bed and closet vary from fully open (pulled to the top), to being down with slats open. Also interesting here is that this may also be a revealing mistake when set lighting appears reflected in the window when the blinds are up.
This entire premise is one huge plot hole since, by law, cops aren't allowed in real life to date, or otherwise ask out, women that they meet "on the job".
The scenes where Carrie gets pulled over and when her and Doug are going home from court shows their car windshield lacking the proper registration / inspection stickers that NY requires. Strange that when Carrie gets pulled over that she isn't ticketed for that offense. Then in the scene where Carrie and Jeffrey leave the restaurant, her car has the appropriate stickers.
When Doug (Kevin James) is talking to Carrie (Leah Remini) about going on a "date" with the police officer to try and get out of a ticket he says "Leah, you're an attractive woman... we knew we would have to use that sometime". Not a beat was skipped on him not calling her by her character name of Carrie.