If I wanted to play an RPG, I'd play an RPG. The draw of multiplayer FPS's is the level playing field. The only difference between a new player and an experienced player is skill. Having to grind in an FPS to unlock the best weapons ruins the fun.
Biggest offender: Battlefield 2142. In this game, there are 4 classes, but they all start out with a gun, a pistol, and a knife. You have to unlock grenades, you have to unlock class features like med packs, defibrilators, you have to unlock the better weapons, and you have to do this with points. What's more, it doesn't happen even remotely quickly. Here's why it's worse. If you're starting out in this game, you're competing against people who not only have played the game a lot, but have all the best unlocks, making the gap between you and them even wider.
Moderate offender: Team Fortress 2. This isn't as much of a problem in TF2, because the default weapons are useful. The unlocks usually have some defecit to balance out their advantages. For example, Natascha, the unlockable minigun, has a 25% slowing effect on whatever it hits, but it does 50% less damage. Here's the problem. The two ways to get the weapons are to either grind achievements (which never, EVER come up in regular play), or just wait for them to be randomly found. This promotes a different kind of grinding, however. People either elect to sit in an Idle server, or use an idle program (which valve frowned upon, and invalidated all unlocks gotten by that method), rather than just enjoying the game.
Lesser offender: Battlefield 2. This game had 7 classes, but unlike its sequal, all the specials of each class are unlocked right out of the gate. The only unlocks are a different primary weapon for each class. The unlocked guns aren't much different from the defaults, however, and not having the unlocked weapons isn't really a defecit. Each class can still perform its duty, regardless of weapon.
2. No spectator mode while dead
If I die, I do not want to spend the 15 or 20 seconds before the next spawn staring at the sky, ground, or a black screen. If I'm not alive, I want to be looking at other people who are alive. If I am not bored, realism is an appropriate sacrifice.
Worst offenders: The Battlefield series. I know you're looking at the sky because there is a chance you may be revived, but it is no less disorienting to be thrown back into the action from a spectator's view than from a view of the sky.
3. Shitty lobby systems
Lobbys aren't a bad idea. They give you time to get a game set up, and you can start the game when all your friends are in. Furthermore, matchmaking for pubs on some games is a great idea, and properly implemented, works very well. But a lack of options can make this system maddening.
Worst offender: Call of Duty Modern Warfare 2. This game is banking on multiplayer, as the single player campaign is 6 hours long at most. So thanks, InfinityWard, for removing dedicated servers and making all multiplayer work on a lobby system. The wonderful thing about dedicated servers is there are infinite options. People who own the servers choose the settings that fit the server's playstyle, and also can administrate the servers to get rid of hackers and douchebags. Now that's all gone. This also means pings will inevitably be higher and more eratic. Worse, players surrender control of their gaming experience.
Moderate to Lesser offender: Left4Dead and Left4Dead2. Lobbys are a good idea for pubs and friend-only games here. The problem is, you can't control which server you play on, so you may end up on a strangely modded server, or a server with different than usual settings. If you want to connect to a specific server, you have to mess around with configuration files and the console, which is a lot of hoops to jump through to play the damn game on your own server. My friends and I usually end up hosting locally and waiting 3 minutes for the pings to calm down.
4. Regenerating health
I'd love it if a game would come up with a good system for dealing with getting wounded. I don't know why we can't use health packs anymore. Sure, picking up a box with a red cross on it and having it instantly restore your health is not very realistic, but neither is crouching in a corner and sucking your thumb until your vision clears. It breaks flow.
Worst offender: Any curent-gen game.
So there's a list of four things that annoy me. I'm off.