In Harry Potter, are there ways to reveal if a person is under the effect of Polyjuice Potion? Are there ways to identify its use (with a spell, maybe)?

When Harry, Ron and Hermione went to the Ministry under false identities was there a chance that someone could have found out who they really were?

There doesn’t seem to be any known spell that reveals Polyjuice.

When Dumbledore realizes Moody isn’t actually Moody, he doesn’t use any spell on him to find out if he’s using Polyjuice. In addition, he doesn’t use any spell to force him out of his Polyjuiced form. Instead, he simply waits for the Polyjuice Potion to wear off to see who the fake Moody was.

“But I think, in the excitement of tonight, our fake Moody might have forgotten to take it as frequently as he should have done … on the hour … every hour … we shall see.’

Dumbledore pulled out the chair at the desk and sat down upon it, his eyes fixed upon the unconscious Moody on the floor. Harry stared at him, too. Minutes passed in silence …

Then, before Harry’s very eyes, the face of the man on the floor began to change. The scars were disappearing, the skin was becoming smooth; the mangled nose became whole, and started to shrink.”
_{^{- Harry Potter and the Goblet of Fire, Chapter 35 (Veritaserum)}}

In addition, the booklet that the Ministry hands out on protection against “dark forces” gives only security questions as a way to detect impostors using Polyjuice. If there was a spell that detected it, they’d likely mention it, even if it’s a possibly difficult spell.

“4. Agree security questions with close friends and family so as to detect Death Eaters masquerading as others by use of Polyjuice Potion (see page 2).”
_{^{- Harry Potter and the Half-Blood Prince, Chapter 3 (Will and Won’t)}}

It doesn’t seem like the people at the Ministry would be able to figure out that Harry, Ron and Hermione were impostors using Polyjuice unless they noticed them acting oddly. The only thing known to “undo” Polyjuice is the Thief’s Downfall, which isn’t a spell and only is seen in Gringotts - it may not be replicable.

The Marauder’s Map would reveal their true identity, similar charms may.

When he was using Polyjuice to disguise as Moody, the Marauder’s Map still showed Barty Crouch Jr. as “Barty Crouch”.

“I used the map I had taken from Harry Potter. The map that had almost ruined everything.’

‘Map?’ said Dumbledore quickly. ‘What map is this?’

‘Potter’s map of Hogwarts. Potter saw me on it. Potter saw me stealing more ingredients for the Polyjuice Potion from Snape’s office one night. He thought I was my father as we have the same first name.”
_{^{- Harry Potter and the Goblet of Fire, Chapter 35 (Veritaserum)}}

The J.K. Rowling writing on Pottermore states that it uses impressive magic, including the Homonculous Charm.

The magic used in the map’s creation is advanced and impressive; it includes the Homonculous Charm, enabling the possessor of the map to track the movements of every person in the castle, and it was also enchanted to forever repel (as insultingly as possible) the curiosity of their nemesis, Severus Snape.
_{^{- The Marauder’s Map (Pottermore)}}

While it is fairly advanced magic, it’s likely that the effects could be replicated.

It's possible to remove the potion's effects with The Thief's Downfall, as seen in the seventh book when they rob Gringotts:

[T]o Harry's horror he saw that [Hermione] was no longer Bellatrix; instead she stood there in overlarge robes, sopping wet and completely herself; Ron was red-haired and beardless again.

‘The Thief’s Downfall!' said Griphook, clambering to his feet and looking back at the deluge on to the tracks, which Harry knew, now, had been more than water. ‘It washes away all enchantment, all magical concealment! They know there are impostors in Gringotts, they have set off defences against us!'

This wouldn't tell you that Polyjuice specifically was used, however, since it removes all enchantment and concealment, but it would be pretty obvious something was used to magically alter appearance.

Possibly Secrecy Sensors and Sneakoscopes

I would argue that Secrecy Sensors can detect Polyjuice Potion. First, it would make sense given the description of Secrecy Sensors in Chapter Fifteen of Half-Blood Prince:

"Look", sighed Hermione, "Secrecy Sensors detect jinxes, curses, and concealment charms, don't they? They're used to find Dark Magic and Dark objects.

While a concealment potion may be different from a concealment charm, the purpose of the Sensors is to detect concealment so it would be reasonable that they detect potions as well. Furthermore, the Sensors appear to be the only security check applied to students in Half-Blood Prince. From Chapter Eleven:

Well, Filch ran over all of us with Secrecy Sensors when we got into the entrance hall.

If Secrecy Sensors could not detect Polyjuice Potion then it would seem that there would have been nothing preventing a Death Eater to enter Hogwarts disguised as a student. Considering that Hogwarts had already housed a Polyjuiced Death Eater for an entire year, failure to check for this would have been gross negligence (though this is Dumbledore we're talking about).

More importantly, there is potential evidence from Barty Crouch Jr. (disguised as Mad-Eye Moody). In Chapter Twenty of Goblet of Fire he introduces Harry to his Dark Detectors, one of which was a Secrecy Sensor:

"What's that?" Harry asked, pointing at the squiggly golden aerial.

"Secrecy Sensor. Vibrates when it detects concealment and lies... no use here, of course, too much interference – students in every direction lying about why they haven't done their homework. Been humming ever since I got here.

Note that he mentions that Secrecy Sensors can detect lies, which was not mentioned in their description in Half-Blood Prince. We also never find anyone using Secrecy Sensors when they want to determine if someone is lying, though there were a bunch of opportunities for this throughout the series. Furthermore, we find that throughout Half-Blood Prince Filch was able to use a Secrecy Sensor without having any problems with interference (and presumably there was no significant change in the homework-lying habits of students in the two year interim).

I would therefore argue that Crouch Jr. lied to Harry about the Secrecy Sensor. The Sensor was clearly activated when Harry was there, which required an explanation:

In the corner on a small table stood an object that looked something like an extra-squiggly, golden television aerial. It was humming slightly.

Since neither of them were ostensibly engaging in jinxes, curses, concealment charms, or Dark Magic, Crouch had to come up with an alternate explanation, so he blamed it on students lying about homework and Harry fell for it. In truth, though, the real reason why it was humming was that it detected that Crouch Jr. was impersonating Mad-Eye Moody.

Similarly, Crouch Jr. explains that his Sneakoscope has been whistling non-stop:

I had to disable my Sneakoscope because it wouldn't stop whistling. It's extra-sensitive, picks up stuff about a mile around. Of course, it could be picking up more than kid stuff," he added in a growl.

Compare this to the description provided in Chapter One of Prisoner of Azkaban:

If there's someone untrustworthy around, it's supposed to light up and spin.

Throughout the rest of Prisoner of Azkaban the Sneakoscope is constantly acting up, and they assume that it's broken. However, I would argue that it was actually picking up Peter Pettigrew pretending to be a pet. Consider that in Harry's house it seemed to work fine:

Harry put the Pocket Sneakoscope on his bedside table, where it stood quite still, balanced on its point, reflecting the luminous hands of his clock.

And in Goblet of Fire (Chapter Twenty-Three) it seems to have gone back to working fine:

The reason they were extra-knobbly was that Harry had been using them to cushion his Sneakoscope for over a year now. He pulled out the Sneakoscope and handed the socks to Dobby, saying, "Sorry, I forgot to wrap them..."

Similarly, I would argue that Crouch's Sneakoscope was picking up on the fact that he was impersonating Moody, and because he couldn't tell this to Harry he made up another excuse about why it was acting up.

Based on the above, I think it is possible that there are certain magical objects – such as Secrecy Sensors and Sneakoscopes – which could detect that someone is impersonating someone else via Polyjuice Potion. However, it would seem that they do not actually confirm that the specific method is Polyjuice Potion; you would still have to figure out yourself that that was what the instruments were detecting. And they also do not actually reverse the effects of the Polyjuice Potion. But merely knowing that there is some trickery or concealment involved would often be enough. If the instruments detect something you could confine the suspect until the possible potion would wear off, or you could decide to question the suspect in such a way that would confirm the impersonation.