During one of their first appearances as 'Cops' Damon Wayons Jr jokes he feels like Danny Glovers character, Roger Murtaugh in Lethal Weapon. His dad, Damon Wayons Sr would later go on to play Roger Murtaugh in the tv series remake of Lethal Weapon.
Jake Johnson and Damon Wayans Jr. both work on New Girl (2011) together. Nick Miller, Jake Johnson's character on New Girl, has the same surname as Justin Miller, Damon Wayans, Jr.'s character in Let's Be Cops. Rob Riggle has also appeared on New Girl as Big Schmidt.
A picture on the webpage for this movie shows both officers running on a beach behind or next to women dressed in bikinis, (possibly referencing a scene from the show Baywatch), although this was never shown in the theatrical release of the movie.
While not all officers in a department will know every other officer generally speaking, it is highly likely that all officers will know the officers, especially supervisors (Sgt.), at least within the same division, especially when working the same shift, so it would be highly unusual for the real officers to not know the pretend officer and Sgt. were fake.