Even some of the Hogwarts professors or students could catch Dumbledore. Maybe a curious student stumbles upon Dumbledore in a restricted area where he's doing something strange. Or a professor who has a different view on how to run the school catches Dumbledore in the middle of an action that they think is wrong for the school's environment.
There's also a chance that Dumbledore gets caught by a group of rogue magical creatures. For instance, if he was exploring an area that was supposed to be off - limits to wizards and the creatures there saw him as an intruder. They might not be as rational as wizards and could hold him captive without really understanding who he is.
In certain fanfictions, Dumbledore could get caught in a lie. Maybe he told the students one thing about a particular magical artifact, but then was caught when it was revealed he knew more than he let on. This would create a lot of drama as the students and other faculty members might lose trust in him for a while.
Aspiring young writers who are fans of the magical world. They see Dumbledore as a rich character to base their fanfiction on. They could be students who are inspired by the detailed world of Hogwarts and want to contribute their own ideas about Dumbledore through writing.
Maybe it's a strict teacher or mentor in their world. If they are breaking some rules, like skipping important training or lessons, the teacher or mentor could catch them. This would then lead to some form of punishment or a lecture about responsibility in the 'nico and will get caught fanfiction'.
The Ministry of Magic could be responsible. They might be jealous of Dumbledore's power and popularity. They could see him as a threat to their own authority and come up with some false charges to arrest him. For example, they could claim he was hiding information about a dangerous dark wizard.
One possibility is that Dumbledore gets caught spying on a group of Death Eaters. This would put him in a very dangerous situation as the Death Eaters are extremely cruel and loyal to Voldemort. He might be tortured for information about the Order of the Phoenix. However, Dumbledore is very resourceful and would probably be able to hold his own against them for a while, giving his allies time to figure out a rescue plan.
Maybe it was her husband who caught her. If she had promised to spend the day with him but instead was chatting with an old acquaintance for too long, he might feel like he 'caught' her in the act of neglecting their time together.
Creatures that have been wronged by Dumbledore's decisions in the past could side with Rumple. For instance, if Dumbledore once restricted the rights of house - elves, the house - elves might assist Rumple in his revenge plan, believing that Dumbledore needs to be taught a lesson.
It could be Chiron, the centaur. He's always keeping an eye on the campers and would likely be concerned if he caught them up to something. He might give them a stern talking - to and some extra chores as punishment.
Hermione would be a likely supporter. She is always loyal to Harry and if he presented her with evidence of Dumbledore's wrongdoings, she would probably side with him. She has the intelligence to help Harry strategize and find ways to expose Dumbledore. For example, she could use her research skills to dig deeper into Dumbledore's past.