Polygraphs are not used in interrogation (where "interrogation" is "interaction done with a suspect with the goal of obtaining a confession", and "a confession" is "the suspect's own testimony, that gets written down and replayed in court.") All evidence obtained through a polygraph is inadmissible in court, so it's actively counterproductive to use a polygraph if you want a confession. (IIRC, if someone does confess under a polygraph, you need to take the polygraph away, let them calm down, and then ask them to confess again.)

Polygraphs are used for two investigative purposes:

1. To attain leads for investigation. This is basically tool-assisted https://en.wikipedia.org/wiki/Cold_reading. You take a person, add some probative questions, see what makes them nervous, and then dig in further on those topics. Nothing they say can be used as proof of anything, but it can sure guide you to go have a closer look in their bag/at their ID documents (TSA); or to ask the friend they mentioned to come in as a witness; or to try to get a warrant to search their vacation home. (The statements made under polygraph aren't admissible to get you the warrant, either, so you'd need to find some other probative evidence before doing that last one. Usually this is when police would start stalking someone to obtain a DNA sample from a gum wrapper.)

2. To eliminate potential suspects (or potential witnesses!) when your pool of People of Interest is huge (e.g. when a murder occurred in public in Times Square.) A polygraph is a very weak form of exculpatory evidence: it allows you to say that some people are just less suspicious than others, without letting stereotypes guide you in that judgement. If you have 400 PoI and you need to decide who to look into first, batching them through a five-minute polygraph session is an easy heuristic for ranking them (especially when combined with other ranking factors, e.g. a criminal-record check.) It's also pretty good at weeding out "witnesses" who didn't really see anything but just like attention.

Polygraph findings can't really be "wrong" in the #1 use-case. At worst, a polygraph-obtained lead will be zero-information noise, and you'll waste time investigating it. But a polygraph used this way will never cause the wrong person to be arrested/convicted.

Polygraphs can be wrong in the #2 use-case, but only in the sense that they might cause an investigation to be derailed for months/years because someone was eliminated early when they shouldn't have been. (This is why it's important to enforce the idea that it's weakly exculpatory: i.e. polygraph findings can be used to rank the "interest" of your Persons of Interest, but not to entirely eliminate them from the PoI pool.)

Where you see polygraphs really "go wrong" is not per se a failing of the polygraph itself at all, but rather it's the common failing of all police investigation: the wrong-headed thinking that you can convict someone by playing Guess Who, i.e. that if you eliminate all but one person, then that person has to be guilty (and then doing a bunch of motivated reasoning to build weak circumstantial evidence into a case against them.) Polygraphs are often used as one of the tools of this wrong-headed pursuit, allowing a biased investigator to justify a winnowing-down of a PoI pool to just the person or set of persons they personally believe are guilty.

But you don't fix that by taking the polygraph away. You fix that by firing those people.