1. The lag compensation / sync issue. I am old so I am not up to date on all the technical jargon but to me it boils down to this. Other players are able to see me before I see them and kill me even if in my view I have already made a corner or gotten my shots off first. I am not an exceptional player, more of a middle of the road kind of guy but I know unfair advantage when  see it. This makes the game very frustrating and forces me to play in a style that I am not a fan of. The only way I can get a decent K/D or points is to be the camp, move, camp player that every one hates. Even when using this tactic I do not get huge kills because once again they see me before I see them and Bam I am dead. I would much rather be able to run around all willy nilly and have a nice fun fast paced game but it just does not work with this game.
2. The spawn system is horrible. Nothing like respawning in the midst of the other team, not with some other teamates by your side but just you all by your lonesome. Or running around having a good old time and a bad guy spawns directly behind you. Awesome,not!
3. The lack of dedicated servers, really? You folks have made a ton of money off this franchise but we are to believe that you can not afford to have dedicated servers for these games. It seems this is an easy way for you folks to shrug off the responsibility of policing the players. If you had dedicated servers I would think you would be able to install a program to detect boosting, modded controllers and what not. But instead you put the burden on the players,nice.
4. Let me start by saying I play Hardcore mostly so this topic relates to it. Richochet, a cheap fix to a real problem that is not even supported by your game and was never meant to be. It basically makes Martyrdom and Dead mans hand useless and dont even get me started on having a fellow teamate using Assasin Pro. What exactly was wrong with the "three teamkills and you are kicked method". Not a very well thought out solution.
5. Lack of support. I posted a question in the support forums a while back concerning a problem I was having with my screen locking up and having to reboot the whole system then not being able to log back into the game. I still have not received an answer. Completly useless.
6. COD Elite. I got suckered into buying Elite, not very impressed at all and I will not be renewing that membership. Basically the only difference between the paid version and the unpaid version is that I do not have to pay for future DLC, but whos to say I will even be playing the game anymore by the time it comes out. All the paid for content should have been availalable at the time of the game release, not 3 months down the road. Dont even get me started on the whole thing not even working for the first month, really dropped the ball on that one I must say.
7. Lack of game modes for us lowly Hardcore players. Really? No more CTF, Headquarters,FFA, Team defender. I do not understand why we cannot have the same playlist as all the core games,lame.

To be totally honest I really like the game, The campaign is pretty awesome and I really like the Survival / Mission modes ( although it would have been stupendously awesome with 4 players instead of two ). I like the killstreak system, the prestige system, the guns and the weapon ranking system and I even like most of the the maps. But of all the grievences I have stated above, the lag / sync compenstaion system would be my number one complaint.