One of the more difficult things to admit as a referee is when you make a mistake. We like to think that mistakes are mostly of the "oops, didn't quite mean it that way" variety, but sometimes mistakes can be much bigger than that.
Probably my earliest big mistake came when I was running a Chivalry & Sorcery adventure for a bunch of players at my local game club. They had encountered a barrow wight, and I ran through the entire encounter without taking into account the serious "fear" ability that the undead creature had. The party went away with a bunch of loot, and I felt bad about it. So when I went back to read up for the next adventure, I came across the rule about inflicting fear - and decided to re-run the entire encounter at the next club meeting. There were howls of protest, but some of them actually went along with it. Looking back on it 30 years later, I still recall this as a moment that I'm not at all proud of. Re-running an encounter? My older self says, "suck it up and learn from it for next time."
Somewhat more recently, I ran a D&D 3rd Edition campaign, with players who were...casual, shall we say, about in-game consequences of their actions. It all came to a head when the paladin in the party started to bargain with the rogue in the party about how to quietly steal from (and possibly murder) a third player-character. The player of the paladin seemed shocked that her deity just might have ideas about such dishonorable and ignoble behavior - and the rest of the party seemed as shocked as she was. That group fell apart for that reason, amongst others. It made me think carefully before starting a long-term campaign with people whose gaming style I was unfamiliar with.
Not that long ago, I ended up running an espionage game that was supposed to transition into an Infinite Worlds campaign. We had all gone to see The Bourne Identity, and my players were really pumped up about running spies and doing covert operations. What I hadn't counted on was the complete disinterest on the part of the players to do any real world research about the organizations their characters worked for (CIA, MI5, the Mossad, etc.). The mistake I made was then in providing them with NPCs who would feed them information. Then practically every adventure session started with, "I call home; what do I find out?"
I'd love to be able to say that I've learned enough from all of these experiences (and many others) to have a coherent idea of What It All Means, and How To Improve Your Game in Three Easy Lessons, but it would not be true. The reality is that I find myself having learned from some of these mistakes and doing a bit better - but that's about it. Since I just moved, I don't have a regular gaming group right now, so I know I'm a little rusty....
...which means I'm likely to make a mistake or two in the future. Here's to not rolling a 1 on my next saving throw!