This question came out of another post on here of mine, so there may be some similarities. An answerer/commenter on that question suggested splitting it off, so here goes:

I'm a new DM, using Lost Mine of Phandelver to run a campaign. During the course of this adventure, I discovered what I deemed to be a plot hole, in that the path to Cragmaw Cavern is portrayed somewhat as being unsuitable for the wagon, yet the wagon is needed to move loot. This isn't the point, just background.

My solution was to say that "when you entered the clearing, you also saw another path which is wider and suitable for the wagon". My question here then is whether retroactively adding a feature is an acceptable/appropriate DM action. I know the DM makes the world, and DM word is law (to a point). But realistically, should the DM ever do this, go back and "correct" something in the past, or should they find another way to handle it?

My concern was that the PCs either wouldn't or couldn't find another solution, so I gave them an option. Is it okay to retcon like this?

The PHB supports what you did.

Ultimately, the DM's authority extends even to this.

Ultimately, the Dungeon Master is the authority on the campaign and
its setting, even if the setting is a published world. (PHB, p 6)

But it's still best to discuss it with your play group

"Because I said so" does not always sit well with a given group of players. Whenever you retcon something in a game -- not just in D&D -- I have found that it is best to (1) discuss it with the players, (2) explain why, and (3) get their buy in. If they don't buy into it, you've got to consider "how important is this retcon to our continued campaign?" It is best to arrive at an agreement, or "get on the same page" before you start the next session.

Sometimes, we DMs and GMs fess up and tell the group: "eh, I think I made a boo boo there, here's how it works from this point forth. The gods were crazy that day."

Or something like that.

• We ran into that in our group last Monday night. I allowed a player
  to cast sanctuary and firebolt in the wrong order (he should have
  gone firebolt/sanctuary to avoid sanctuary dropping from the attack)
  but since he's new to the class, and I knew what he was trying to do, and it was good for the party for him to do this, I said after the battle "Yeah, it worked out this time ... but remember, going forward, it is supposed to work like this explained the mechanics." We are on the same page.

Notes:

• 
  retcon is a term often used to describe what you did with the
  retroactive change.


• 
  

  You may find this question and answer "Is the DM always right?"
  useful when dealing with some situations as the DM.

  
  
  

  _{On a humorous note: if the DM's wife disagrees with the DM, can the DM ever be right? grin}

  
  

You're allowed to retcon, although more nuanced solutions are usually preferable.

A retcon—retroactively changing something—is always within the DM's power in D&D. In one campaign I played in, the entire party was killed, and the DM rolled it back because it would have made for a disappointing ending to the campaign. You always have this ability, and there are situations when it's the best choice.

However, this power is usually kept in reserve for emergencies, for a few reasons:

• It can undermine the players' sense of continuity in the world. It feels a little jarring sometimes to be told that you can't rely on your recollection of the game's events, or that something you achieved didn't happen after all, and so on.


• It can feel unfair, since players may say, "If I had known about X, I would have done Y instead" or "If X had happened, I should have more hit points left", and so-on. You can end up with a chain of demands for do-overs, which is a very awkward mode to play in.


• It feels like a violation of the "show, not tell" rule of story-writing. You ideally want the players to explore the world organically, rather than just have their past events dictated by the DM.

In this scenario, you did well to think on your feet and find a solution to a problem.

However, a more elegant method of retroactively introducing an element is to place it such that the PCs never saw it before until now, so that their past perception isn't inconsistent.

For example, perhaps the wider tunnel was hidden from the entrance and the player characters didn't see it on their way in. Or, perhaps its location is known to a helpful NPC, who shares it with them.

There are several related issues swirling around your question. Let me try to disambiguate them and answer them separately:

Can I Retcon?

Yes. You're the GM. It is fundamentally the job of the GM (in D&D 5e) to decide what the players see, sense, and experience about the game world, and it is fundamentally the job of the GM (in D&D 5e) to decide and determine what the world is

I'm unaware of a corresponding passage in the DMG (oddly enough) but the PHB states clearly on page 6:

Ultimately, the Dungeon Master is the authority on the campaign and
its setting...

In D&D, this is nearly absolute, up to the limits of the players getting up and walking out of the game. It includes retcons, even though that is not strictly what that passage is talking about.

Should I Retcon?

This is a dicier question. Strangely enough, this time, it is the DMG putting the brakes on the situation, on page 4:

Consistency is a key to a believable fictional world.

This quote is not really addressing the issue of retcons directly, either. But it is easy to see how this applies-- a retcon, by its very definition (a portmanteau of 'retroactive continuity') is a break in the consistency of the game world you are creating or, in this case, directing.

The thing about retcons is, they can be very jarring for the players who experience them, and individual players and GMs have widely differing tolerances and reactions to them. I've seen players react very badly to even minor changes like this. In the worst cases, it trains them not to trust their senses as you narrate them, and jams their ability to decide what their characters think and feel about their own characters and decision making processes.

But I've also seen players (when they hear me muttering to myself about having messed up my own plan) offer to roll back and retcon a major combat encounter if it would help me out. (I was stunned.)

My best brief answer to the "Should I?" is, with great caution, don't wait very long to do it, and be upfront about it.

Can I/Should I... With Pre-Published Material?

Unless you're in a special situation like running a convention slot or are in some other way subject to an even higher authority than yourself as GM, it does not matter whether you retcon your own personally designed scenario in your own personally designed world, or if you are running something otherwise completely per print from a published adventure.

You're still the GM. You're still the authority. The same caveats about player reactions apply in exactly the same measure.

If an authority for this is needed, the full and complete quote from the PHB is actually:

Ultimately, the Dungeon Master is the authority on the campaign and
its setting, even if the setting is a published world.

(Emphasis mine.)

A Divisive Issue

Whether or not significant retcons are okay is a thing about which people have differing stances. Some people see retroactive changes—ones of which the players weren't informed when the PCs should've spotted the relevant things—to be unacceptable due to depriving agency by way of denying the ability to react to the thing/opportunity/etc.. Others consider all methods fair so long as they make the story interesting. And of course what counts as making things interesting is subjective.

On a superficial level, it may seem that traditional games are more inclined towards a more 'stable' interpretation of the PCs' surroundings, and that indie games are more inclined towards accepting even drastic retcons. This in turn would make it seem that the D20 family of games, as the epitome of traditional games, would lean against retcons. But then again, Quantum Ogres are a D&D meme that is to a fair extent critical of a player who won't accept even a potential covert retcon (i.e. one which cannot be meaningfully proven unless the player is either telepathic or read the GM's notes). So, as they say, all crayons taste different.

Know Your Players

Either stance can lead to fun campaigns for the right 'target audience'. But it's important to know whether a given audience is in fact the target of a given way of handling such matters. E.g. if some or all of your players happen to want a very objective world where things don't change except as a result of in-setting events or actions of PCs and NPCs, then you may have a problem on your hands when such players notice a retcon.

So it's best to make sure you and the players are on the same page. Before a campaign, or, since you're already GMing, during some chat between sessions, try bringing up the subject and finding out what the players find fun. If your preference and the players' don't match (and both of you have strong preferences), you may need to either find a way to achieve a compromise, or consider a change of roster.