The first thing you'll notice is how terrible the game is for new players. They start off with the worst weapons and are then placed against players with more experience, more skill, and more unlockables (you'll learn to hate the P90 with the red-dot scope, don't doubt that). How can a big, successful game company like Infinity Ward miss something as basic as balanced matchmaking? Rhetorical, don't answer that.
And what's with the grenade indicator? It's wholly useless in multiplayer, and only slightly worse than it is in the single player. It doesn't indicate proximity to a grenade at all, and many times won't register a grenade at all before you die inexplicably. The grenades themselves are a bit overpowered, though the simulated mechanics seem realistic enough; maybe I'm just frustrated by getting eliminated from a Search & Destroy or Headquarters round by a grenade thrown completely at random. The flashbangs and stun grenades are pretty fun, especially when you stun yourself from around a corner but fail to stun the target because... the game hates you or something.
This brings me to my biggest peeve: hit detection. I've played a lot of FPSs online in my day, but CoD4 has some of the most inaccurate hit detection I've ever seen, for both bullets and grenades. From your screen, you may unload ten rounds into your target before they get that last bullet on you, and while the kill cam loads, you expect to see the assist points flash on your screen for doing so much damage to them; after watching the cam, however, you realize that the server didn't register more than a single bullet. Could it be lag? Maybe, but that makes the connection indicator more useless than the grenade indicator, as I've never been below 5 bars. It's also common to get yourself behind cover and continue to get pelted by bullets: many of the more powerful weapons can push through surfaces like glass or wood, but pistols should not go through sheet metal.
Wow, that feels good. Onto the things I liked.
The maps are incredibly well balanced. Choke points are frequent, but flanking is always an option; cover is never is short supply, but camping is no easy task (unless you place a claymore at the top of the single ladder leading to your spot... that's kinda broken, but not too hard to work around); each map has a unique character, but a strong sense of balance between close quarters and long range is found in all maps; the variety of game modes is sure to make any kind of player happy, regardless of style, skill, or experience. Personally, I feel these pros completely outweigh the list of cons, but I feel games are getting to the point where certain errors can no longer be tolerated.