I have a few topics, but after my game yesterday this is the most prevalent in my mind.
Within my own game, a couple things I've been hinting at a few things that near as I can tell, completely flew over the PCs heads. (though probably more esoteric then normal, because ultimately unimportant.) I've had a character always unsure of if the PCs were secretly sort of allies of his own group, or an enemy group, the truth is they're the latter, but the two parties have never really talked honest enough for this to slip and turn into a fight. Then, as a joke at that, one of the PCs made a very, very good roll, at their seduction skill at that!
On the spot, I decided to roll with it, and instantly develops at least a small crush, and started spilling information that my PCs that hopefully filled in even more for them. In addition this gave me the perfect chance to just be overt and offer them a way to do something that will drastic power up their characters that I've been hinting probably for years, but am sure they'd never of caught on to on their own. All from one roll that was completely unexpected. This has got me thinking that this is a fairly common occurance in RPGs.
This should be obvious, but something so often missed by people, RPGs are run by dice, and when certain rolls lead to disaster or critical success, it can change your plans in ways words really don't describe. A good example that goes the other way is an episode of Horror on the Orient Express by the staff of Yog-Sothoth.com (Their episodes are highly recommended to anyone interested in RPGs or Call of Cthulhu) where a little detail between parts of the adventure, they need to deal with stubborn animals on a small train cart leads to a horrible series of rolls resulting in a character losing an eye, and another becoming a disfigured morphine addict, and these events alter the way things had been going.
The bitch of it is predicting these things, when your main antagonist is meant to be the god of schemes and even a casual glance at your DVD collections of Death Note and Code Geass will reveal you like things to go as had been planned the impact and frequency of luck can make it very, very difficult. But there's dirty tricks to solving that, most of the time.
The main lesson to take away, I suppose, is very important skill when it comes to being a GM in tabletop games and the freedom they offer, you need to be able to roll with sudden, unexpected surprises.
Don't worry if you lack this skill though, you'll learn quickly.