DMs are human. (AI DMs are for a different discussion, not here.) Humans err.

When a DM (your campaign's DM or you as DM) makes a mistake and admits/knows it, what happens from there?

• What do you, as a DM, do when you realize your mistake?
• What do you, as a party member, prefer to happen when your campaign's DM admits a mistake?
• What about when a DM (your campaign's DM or you as DM) realizes something was wrong for several encounters or rounds?

Feel free to specify contexts for nuanced replies.

I'm going to avoid the topic of DMs who either don't see their mistakes or won't admit their mistakes. That's already discussed elsewhere per-incident.

(Not based on personal experience, but based on something I've seen. I'm curious about opinions. No opinion is wrong here.)

“Mistakes are a fact of life. It is the response to error that counts.” - Nikki Giovanni

Mistakes is part of the game so no worries. How i deal with it depend on the nature of the mistake and it's repercussion on the campaign. When i DM and make a small rule or story mistake, i may either roll with it as is or correct it immediately. If it has more significant incidence on play, i may even do a back in time or adapt on the fly. All in all, i try to keep a few things in mind when playing D&D, the fun of all players involved, the campaign's well-being and the impact of the mistake and follow-up actions, if any, on all these aspects.

I'm going to make a mistake too, as a player, so I roll with it like I want the DM to roll with mine. If it wasn't a plot-crucial mistake, then something like awarding some extra XP or spontaneous gold generation seems appropriate if they want to make up for it (if it even needs it). If it's something bigger, like a PC dies or a magic item is lost, etc, the DM offering some sort of retcon or new opportunity to find the thing, or a lowered difficulty to whatever we're doing to regain whatever we lost would be appreciated, if they asked if we wanted to do it and didn't like the story path we'd ended up down.

If you are the players in my group…

Keep acting as though the mistake didn't happen, even though the GM repeatedly says, "That was a mistake, it didn't happen!"

Arrgghh.

If a pc is not dead, and I discovered after the session. I just mention the mistake next session. During the session and a round later, if in the monster favor I give back the HP. If in the party favor. I don't worry about it. 

Depends on the mistake.. If its a minor mistake such as using a spell slightly wrongI'll just roll with it was a player.. That kinda stuff happens all the time from both players and DM, it's expected.. If I catch the mistake as it's happened I'll point it out, but often it's just water under the bridge.. especially if more than a round has passed.. At that point backtracking simply isn't worth it.

If its something major, like a major character/player character dying or some important plot point, I think adventurers and DM should work together to find a retcon.

Fix it, move on.

There is a reason that I write all my homebrew rules out and playtest them beforehand in one offs. IF you mean something beyond a  core rule, like something where my call was off...

fix it, move on.

Standing rule is that it stays until I fix it. You can call me on it, and you get three to five minutes to make your case, and then if I agree it is changed going forward, but time stops for neither god not man. there is no back and forth, and because rules lawyering was a nightmare I dealt with often in the 80's, I never recovered and don't get into big fights or arguments. It is three to five minutes -- and that includes me asking clarifying questions. 

There are no hypotheticals, it is always about the point in question, and that is usually carried forward, because I am not going to interrupt the play to meta-fight. I am willing after a session, but usually not that night, and I like to do research, so a big problem will take time. We go with what is until we know better.

There are two good ways to handle it in my book:

1, if you're able to fairly and relatively easily, just retcon. "Oh right, you do have a magic weapon now, ok that goblin is dead."

2, if you can't retcon fairly ("but if the ranger gets their hp back then we should ALL get it back") or easily ("the goblin should have actually died four rounds ago and we don't all remember exactly how much damage it did in that time"), then I'd just say "well ok, we remember that going forward."

It depends on the cost.

If the cost is superficial, it benefits the party, or ended up with a positive effect on the story, then leave it be. We then decide as a group whether we continue using the inadvertent house rule or use what it should have been then on.

If the cost is too high or puts a downer on the story, then we discuss a retcon. If a character dies, I will offer the player a retcon like they were just  knocked unconscious or some such. I try to fix it.

I had an example of the former last night. The party was returning from fulfilling a quest and failed their checks to find their way home. This lead to them getting into random encounters and taking a longer time getting home. However, no one died, no one lost anything really. This morning, a ranger realised that they'd taken Natural Explorer and therefore couldn't get lost. Oh well, just remember that ability next time, so no retcon needed. It may have been more tricky had someone died as a result (also greyer - it was his fault...should we do retcons for that? I never had to make that call so haven't decided yet).

Honestly, rules mistakes, DM misinterpretations and forgetfulness in combat are things I and my tables prefer to be respectfully called out in the moment so quick retcons/rulings can happen. This includes things up to and including situations involving PC deaths. PC death is not a small thing and can be emotionally charged, but ultimately, it's a game. The stakes for these DM errors are on a game enjoyment level and that, to me, isn't as important as an interpersonal one.

Mistakes that jeopardize player comfort, cohesion, or belonging? That's private conversation territory that needs more than just a quick call-out and retcon. When human relationships and personal comfort are in the balance, that should be a thoughtful, sincere conversation and hopefully involve an authentic dialogue and, when necessary, an apology to the affected people. Make-believe reality can be easily altered after the fact and accepted as true; emotions, relationships, and out-of-game reality deserves more intentional care.