Things about the system that annoy GM's

[Jeff B]

I say these three are your worst headaches:

  Mobility
  Immunity
  Certainty

Mobility applies to any form of unusual movement -- teleport, ultra-high speed, tunneling through stone, flight, underwater ability.  Any of those, used ruthlessly, can give a character great power.

Immunity is anything that makes a character completely immune to a threat -- force field, skin of steel, 100% magic resistance, insubstantial body, and so on.  The character can act without thought to the risk involved.

Certainty is attacks and abilities that always work -- no die roll needed.  Even if these are limited by just a few uses per day, it's still more than enough to destroy the GM's strongest opposition.  The clever player will time the uses appropriately.

That said, my underlying feeling is that you're dealing with players in a "vs. the GM" mentality, which I personally think is an unhealthy RPG culture.  Some players engage in these games not to enjoy roleplaying or create a story with a group but rather to outsmart and humiliate the others, including the GM.  They're acting out a need for domination, rather than a desire for cooperative play.  The solution here is to keep away from such players.  RPG is not (or should not be) a competition to see who can thrash the world the most.  For the most part, players should be prepared to engage in the traps and difficulties set by the GM, as this is the meat of the adventure.

[chronoplasm]

Mobility applies to any form of unusual movement -- teleport, ultra-high speed, tunneling through stone, flight, underwater ability.  Any of those, used ruthlessly, can give a character great power.

It's possible to do these things in a way that's fun for everyone though. I feel that this is actually one of the strengths of 4E (for people that are into this sort of thing).
Such movement can be balanced by limiting usage (encounter/daily movement), restricting it to higher-level play (if levels are used), by making it less reliable (skill checks, such as with "clumsy flight"), and by giving it trade-offs ("overland flight" is faster, but it grants "combat advantage" to attacking foes).

[Warrior Monk]

Personally, for me, it's when turns take too long.
I hate it when a player gets to make ten attacks practically every turn, it slows things down too much. It's also annoying when players have to spend ten minutes looking something up in the book or sorting through all the crap on their many character sheets.
Play should be streamlined.

I also hate having to explain he complicated mechanics of rpgs to someone who has never played an rpg in their life. I wish that these games were more newby accessible.

Me too. Complicated mechanics are ok when you and your party can manage them quickly, either because you are geniuses or used to the system. But in order to make a good fun story, mechanics should be streamlined to not interrupt the flow of the players and GM's emotions. I'm struggling to inject the games I'm working on with a concept I rarely find in RPGs: System Efficiency. By this I mean not just making a system that works and gets you anywhere (any system can do that) but doing it with the less amount of stats, rolls and rules.

Many stats can be done to meant many things at once. Let's say you need resistance scores for players to roll in case their characters get poisoned. You can make it a separated stat so it can be modified by race, for example. More meat for your munchkin players. But then you need to make some extra space for all kinds of resistance in your character sheet. Second choice is to make it a derivate stat, like from constitution score. You still need to make space on your character sheet for that... so why not straight roll the constitution score for that? of course it means less customizable characters, but then its all a matter of balancing your game, whatever you like it to be.

Rolls can also be readed and interpreted in many different ways. So instead of rolling one dice for attack and another for damage, you can derivate the amount of damage from the attack roll. Depending on the dice and system you use, you can even tell in one roll if surroundings result damaged by the attack, or whatever you like.

So, going back to the current topic, Rules can be made just to avoid any major threat to the fun of the game, instead of trying to stop every single different trick players come up with to annoy the GM. Then you would need a rule to avoid unlimited mobility, one to avoid unlimited Inmunity, one for perpetual Certainty and I'll add one more: a rule to avoid Abuse of any mechanic -like, a metagame rule where the player can't solve every problem in a single session using the same plan more than three times. That way you can even give teleportation, ghost abilities and death touch to players, but they won't be able to use them more that three times per session... so I hope they get creative enough to make the session fun.

If you make your setting good enough, perhaps it won't need to be a metagame rule, like in Don't Rest Your Mind, where players have god-like abilities that could cost them their lives if they abuse or don't use them wisely.