And my point is that is becoming less and less as police are in the limelight. I've gone through the hiring process for Farmer's Branch PD, LSU Medical Services PD, New Orleans PD, and (the one I've accepted) a federal one. The only one that didn't call every single one of my prior jobs was the LSU Medical PD. They also require you to buy your own firearm. I'll give a run down on the NOPD hiring process though, since it is a major city and they generally all have the same basic similarities.
First you do an application, this is just your basic stuff.. Mostly they only turn away felons and illegals here. This gets you set up to take the civil service test. You travel down to New Orleans and take that. It lasts about 4 hours, in two parts. They grade the first part instantly and then get back to you on the second part. If you fail the first part, you don't take the second part. After you pass the second part, you get a call for the PT test. Again, you do that in New Orleans. It is easy as hell. After that, you go directly to the NOPD Headquarters and meet your Investigator.
Every potential new guy gets an investigator. They interview you, recorded, and go into everything you can remember. They also do admin stuff like making sure your second application is correctly filled out. You'll be there for about 6 hours. After all that, you take a lie detector test. The one the NOPD uses measures voice stress. Failure to pass this ends your process there. The next day you go for a board interview, where you'll have 4 or so officers from various divisions asking you about yourself and giving you situations. Where the investigator grills you like you're being interrogated for a crime, the board is a lot nicer. They might ask you something like "Do you feel that police officers need leadership qualities?" or "This happened at this scene, you are the first there, what do you do?" After that, you are done while the investigator goes through your work history, including pulling up your entire military history.
Within 2 days of my interview, all the people I had listed as acquaintances had a letter form the NOPD where they had to write a paragraph character statement on me. Every former job I had got called and they asked questions. They look you up in the FBI database, look up your credit report, all that. If you leave anything out, you aren't hired.
This was all pretty standard through all four that I've done, except the LSU one, which, as I said, didn't call anyone.