Years ago in a game that was not DnD a situation arose towards the end of a session where I had to make a judgment on how to apply the rules. The decision I made in that moment (before dice where rolled) resulted in a player death. At the time the players where upset a character had died but had no issue with my application of the rules. 

This was the early days of the internet as a resource for rules lawyering so after the session I had a think spoke to a friend who is also a DM and then went online to her old message boards to ask opinions.

As a result 2 weeks later the next session I explained to the table that I felt I had made a mistake and so as a result the character was not dead, she had managed to cling to life on a single hit point. 

That was a fairly easy thing to correct in terms of the timing (end of session) and since then over the years there have been multiple occasions, some minor some major, there I have made a call in the moment I then decided was wrong.

 For our newbie DMs to get a sense of what they can do when something goes wrong due to an wrong decision they made. 

What are your stories of retconning mistakes you realise you made later in session or between, do you retcon mistakes and hold your hands up or just hope no one notices when you apply a different decision next time.

Note I am not talking situations where you make a decision in the moment and let your players know there and then you will research it and decide a proper rule application for next session in order to just keep the session flowing. 

DMs are human, and humans are prone to making mistakes.  As a DM, your ruling stands at the table, regardless of the rules, even if it is incorrect.  Typically what I do is acknowledge the mistake, and play it right in the future, but I don't retcon unless there is a very very good reason to do so, and when I do, I do it in the easiest way possible.  That never involves replaying encounters that have already taken place.

That said, in this case the end result was a player character death, so I would be amenable to retconning the death itself,  But, that would not mean replaying any action that occurred between the death and now.  I would allow them to begin playing their old character, with any boon they got while playing a new one (major loot, etc), and with any updated levels the other party members gained, but they would simply reenter the story at the current point, and not replay any lost time.

I usually just tell my players what I did wrong and start doing it right, but no retcons. (If it’s something simple like forgetting AC, I’ll fudge monster HP to compensate, but that’s it.)

For example, my players were recently in a deadly fight against some Drow. I realized I’d been ignoring their Sunlight Sensitivity (which I had taken into account when planning the fight), but I just told the players “sorry, but good news is you’ve showed you can handle this,” started using the Sensitivity, and left the rest of the fight as is. If anyone had died, I would’ve considered auto-stabilizing them, but that’s it.

I usually just tell my players what I did wrong and start doing it right, but no retcons. 

This is what I do. I won't retcon things in general, certainly not from previous sessions. But I will say, "This was not the correct ruling, so we will do it this new way from now on, which is more consistent/whatever with the rules."

A few months back, there was a magical item in my game called The Dark Pawn, which looked like a facial tattoo. It automatically attuned to whoever killed the last bearer of the curse, and they had to lose attunement to another item if they already had 3. It also had the line "You cannot willingly commit an act of charity or deliberate goodness." And the last effect was "You have 30 days to remove the mark, or you die." Lesser Restoration and Remove Curse did nothing. There were several longer storyline ways to remove it, but they needed discovering.

The PCs had taken down a BBEG, and one of them had it. He was a profane soul bloodhunter, slowly sliding further and further into evil. He made a bargain with his patron to undertake a ritual to remove it. The ritual involved him going into a kind of demiplane and killing some guys. The key thing was that his patron - a great old one - had only agreed to 'remove it from you.' At the end of the ritual and combat, the mark left him and I rolled a d4 to see which of the other players around him it went straight to.

I thought it would be a really cool moment of betrayal. What I hadn't counted on was that another player had endured a really crappy day at work, and had felt a bit useless in a fight against flying opponents and a darkness spell, where he couldn't really get to grips. The limitations on roleplay (no good or charity) were something he hated. He was genuinely upset by it, but so was the bloodhunter player - he wouldn't have done the ritual if he'd known the outcome. That was intentional on my part (he should really check the wording of pacts with great old ones...) but it was clear that my players were really, really not happy.

During the interim days between games, I spoke with the 2nd player, and pointed out he could take a level in wild magic sorcerer (he was a wild magic barbarian) if he gained 1 point of Charisma. I was willing to give him that point (and all the other players would gain 1 ASI as well as part of the event that was taking place). This was so he would enjoy his character more. I also discussed what the Bloodhunter would have done when the mark tried to jump to his friend. We rejoined the next session exactly where we'd been, but 1 second earlier:

• I asked the Bloodhunter what he would do: He said he'd try to grab the mark.
• I asked the Barbarian what he would do: He said he'd try to stop his friend taking it back. They caught it simultaneously.
• The resultant clash of power between them caused an eruption of wild magic. The barbarian gained his sorcerer level; the great old one demanded the Bloodhunter let the mark go, and he refused, betraying his patron. The patron abandoned him and exploded his heart in his chest... but the flow of newly erupting wild magic from the barbarian/sorcerer flowed into him and his patron became the same wild-magic angel that fuelled the barbarian's powers, rebuilding a new heart for him (he had had a second heart since level 2, as a gift form his patron, so this was particularly thematic)
• The Dark Pawn curse was obliterated in the spew of wild magic
• The great old one is now a major campaign evil, and both characters are very happy with where their characters have gone.

This change around - a retcon of 1 second of game time - totally redirected how happy my players were, created great new plot developments, fundamentally changed the characters in ways that the players wanted to go.

A more recent one, during a battle last week I was making about 16 javelin attacks against a druid who was wildshaped into an eagle. When she got knocked out of it, we forgot she was prone, and hence the other javelins should have had disadvantage. When we realised, we were already done with 12 javelin attacks. I cancelled a crit she'd taken, and the last creature only made 2 attacks (at disadvantage) instead of 4 to balance it out a little. My players are super fine with the fact that as a DM running 14 monsters in combat I'll sometimes forget something like the Prone condition, and we all adapt quickly. The game isn't about rigid rules adherence.

I am definitely a newbie dm. (Canceled my first campaign because I just HAD to give everyone magical, mythical monsters and monkey wizards)

I think Scarloc's call was right on.  If what turns out to be a bad call on the DMs end resulted in player death, that's probably the only situation where I'd consider a retcon.  Plus players do like the "not quite dead yet" when a dead character is actually revealed to be alive next episode session, it's like it's a trope used in other media or something.

But also chiming in that other than a place where my bad call led to a player death, I'd likely just start next session with "I reviewed the rules in that last situation, and made some mistakes, going forward we'll be handling situations like 'this.'"  Now there are also times when I'll bring in novel ways of handling what are in my game "exotic" situations (i.e. mounted aerial combat, high end metaphysics involving the transmigrations of souls, firearms, you know, the usual exotic stuff), in those moments I'll actually have a short orientation "we're going to try this..." explaining the mechanics involved.  I'll get feedback at end of session which will be a factor, but not the exclusively determining factor, in my announcement next session of "I think that went well, let's stick with it" or "So, we're not doing that again."

I view my games a collaborative, and consequently I don't believe my players try to "game" against the DM.  As a result they're often open to trying a variant rule or a newly produced articulation of handling some exotic aspect of play.  Other games, maybe the ones being championed in another discussion where blind dice rolls are I feel being abused, players would probably be hostile to such game changers.  

One thing I'm certain on, if an erroneous ruling actually benefitted a player, I'll explain my error but will not retcon.  They got the "error in your favor" monopoly card and get to keep the winnings in those instances, but I make it clear how it should have played out and will play out if the circumstance happen again.