This is a known plot device called Chekov’s Gun. Where if a gun is shown early in the play, it will be used before the end of the play.
If a witness or a suspect speaks can’t speak English, it’s a fair bet that the cop can speak their language. If not, the police have access to more interpreters than the United Nations, and all of them are hanging around headquarters ready to go at a moment’s notice.
The same is true around the world. Historians agree that if the Japanese had used their police to instead of soldiers to listen to the Navajo code talkers, they would have won World War II.
There is always a point where your most attractive female officer must impersonate a hooker and wander around in super skimpy clothes.
Similarly at least once the cops have to arrest somebody who’s completely naked, but this is always in a wacky scenario and not somebody having a serious disorder.
There is actually a United States Postal Service detective show about the Postal Inspectors. Not mail carriers but they would either work with mail carriers and tag along on their routes, or even covertly tail mail carriers if they suspect their up to foul play. I forgot what’s it’s called but it was airing a few years ago.
The Inspectors, as it happens.
Everyone who is being questioned always answers using the full rank of the police officers, like chief inspector or superintendent after they’ve been told once during their introduction
I enjoyed that show as I actually know an inspector, though I didn’t at the time the show was telecast. They often ended with a warning regarding a postal scam too.
That’s the best part! 
There was one episode of Boston Legal where the police had a prostitution sting where the female cop was absolutely stunning. In court they made the cop dress up like she did during the sting. Like many plots in that series it was ridiculous but well acted and entertaining. For stings like this the argument will always be entrapment. On the show the sting was like an unambiguous example of entrapment that would be given in an introductory law class. It was so clearly entrapment that it would never get to court. But it did give Stephen Tobolowsky a chance to have a great part giving testimony as the lonely John.
South Park did something a little different. But then, that’s not a cop show… 
You must be thinking of Star Trek. Chekov’s Gun was a phaser. If you saw it early in the show you knew it would be used later in the episode.
No, it is an older phrase from the playwright. But that’s still pretty clever.
FYI, Chekov is a character on Star Trek. The famous playwright was named Chekhov.
In more than 50 years of learning Russian, I have never encountered anyone named Chekov, nor met a Russian who has.
It’s a gun used by Sterling Archer that is woefully esoteric.
The soft body armor cops wear will stop high powered rifle rounds. The bullets will not pass through the vest like it’s melted butter.
Also, regardless of what caliber the vest is hit with, the officer will not suffer severe trauma, broken ribs, or even suffer from Solar Plexus Syndrome where he feels like he’s going to suffocate and fucking die! He’ll just flinch a bit as the armor easily absorbs the rounds.
However, if the officer shoots someone in the chest that person will fly up in the air and back 10 feet. And no, that does not defy the laws of physics where the shooter would also fly back 10 feet. What on Earth are you thinking?
I have seen one show, one time feature a scene where after a character took a round in the body armor they had a giant nasty bruise covering their chest. Might have been SEAL Team, I’m not sure. But in any case, I know there has been at least one time where a character didn’t just shrug off a round to the vest.
Contrast this to the most recent John Wick movie where he gets shot dozens of times and hit by several cars. I was in a car accident at the beginning of the year and I was in pain for about a month. And I had an entire car around me protecting me from the impact of the other one! John Wick just raw dogs impact, letting one thing after another smash him through walls while people are shooting him. Those specially-tailored suits he wears must really be something else!
The stupidest thing about John Wick is that in part 2 the tailor realistically tells John Wick that while his kevlar suit will block bullets, “It’s still quite painful I’m afraid”.
This goes completely out the window in Part 4 where guys wearing the same bulletproof suits take dozens of pistol and SMG rounds and don’t even flinch.
Or sometimes it’s played as a fake-out where a main character is shot point-blank, and falls on his back, apparently dead. His partner or love interest rushes to him, and after a beat, his eyes open, he groans in pain, and rips his shirt open to reveal the vest with a couple slugs stuck to it.
To increase the fake-out factor, it’s usually set up beforehand as a situation where he would not have been expected to wear the vest— he was off duty, but ‘just had a hunch’. Or he was about to go out on official cop biz, and his partner says “aren’t you going to wear your vest?” “Nah, it’s 90 degrees out and we’re just going to question a witness”. But he had a last-minute offscreen change of heart, and put it on after all.
If that’s the standard I guess about half the recruits aren’t going to get through the interview.
I read somewhere that back when it used to be mostly or entirely male officers the most junior member of the team was made to do this duty, I wonder where any eyebrows raised when particularly people kept volunteering.
On the subject of guns apparently bullets don’t deflect off walls as you would expect, but travel along them on impact, so sticking your head around a corner during a gunfight is not a particularly good idea.