Zip code 87051 is for San Rafael, NM. They could have used any of a number of "Sterling" cities, off of the top, Sterling, VA has three zip codes.
Jack Danger tells Jake and Charles that the USPIS motto is, "nos custodimus quod lingus, which he translates to, "We guard what you lick" (though a more accurate translation is, "We keep that language"). In actuality, the USPIS has no official motto.
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.
When Peralta pulls Diaz aside to tell her about the suspect getting away an office sign is visible in one shot showing room numbers for various personnel. Room 206 is listed as "On-Call Sargent" when it should read "On-Call Sergeant".
Jake threatens Rosa to give Jack Danger her home address. In all other episodes, none of the squad knows her home address, and as soon as one of them finds out, she moves.
Rosa says that there was a suspect 20 yards away and Jake let him get away. In actuality, the suspect was about half that distance away, but no one corrected her.