Sometimes in a game we as the DM will design these awesome looking magical items and they look great on paper, but when we give them out during game play we often regret giving them out. Sometimes these items are just killers for a campaign or maybe that one adventure you designed up for the night.
You also know the player will make sure his character holds on to it like its gold, knowing that he has an “edge” on things.
I’ve seen plenty of DMs who will try to take it back from the character by throwing all these monsters or even find a way for someone to steal it with a “no chance you will catch him” scenario. I had a person like that, he would give us these awesome weapons one week, and then see what havoc it caused to his game and suddenly took them away the next week. It came down to the point we just started writing things on a sheet of scratch paper to toss in the trash because we knew it was going away. Did we talk to him? Yes, did he stop? Nope.
I’ve also seen some DMs who will just go with it and watch the wonderful campaign he has created crumble and fall apart due to this mistake. I’ve seen this mostly at convention plays and some local gaming store groups. The DM just goes with the mistake and tries to ignore it, hoping the player will come to his senses.
In this situation I would talk to the player on the side and let him know of the mistake, and ask him to kindly give it up, and maybe offer him up something a bit different in exchange. Most players will take the offer knowing that it will help the game play and the story for the DM as well as keep the fun rolling for the group. Face it, we’ve all been in at least one game where one character get this super awesome thing and destroys all. Its kind boring for everyone else.
As the DM, do you have the right to “clean up your mess” or “let the cards fall where they may?”
If you run a low information game, you have your problem solved. Your players determine they have a Dancing Sword, but after realizing havoc it's causing, so you give it 20 charges and every time it's used more than once a day, a charge is consumed. As long as they don't abuse the thing, it can last a long time. If it turns into their new go-to solution for every nuisance encounter, then they will quickly find themselves with a regular magic blade.
I tend toward keeping magic-items on the weak side in my games to begin with, however I suspect if the problem did come up, there could be logical in-game ways that the world itself will deal with an imbalance of power just like in the real world. Maybe monsters start banding together to form alliances for mutual protection against that overpowered weapon the PCs have. Maybe the monsters put a bounty on "that pesky human wielding item x." Maybe the monsters, after a reasonable time, develop a countermeasure to the item is. Or perhaps the local monarch is disturbed by the sudden excess power the PCs have and his paranoia slowly begins to turn into action. But I don't think I'd ever take something away (in godlike fashion) once the PCs acquired it. And rather than thinking I'd broken my campaign, I'd just let the world run its course and allow the redress of the power imbalance to occur naturally as it would in the real world.