I personally have had the following issues with Bad Company 2:
1- Medics: Now don't get me wrong, I love being a medic, it's a great satisfaction knowing that your success and contribution to the team is measured by more than just how many headshots you can pull off (and the occasional 'thank you' for your efforts makes it somewhat rewarding for me) but the games that tuned into my altruism mostly had one thing in common amongst their medics, they were mostly non-combatants and relied on their allies for protection (Team Fortress 2, Quake Wars, to a certain extent I could put Left 4 Dead in here). Then comes along BC2 with the idea of not only shall we make Medics a full blown combat class, but we shall give them the biggest guns in the game and make it possible for them to out perform every other class (anyone who's had to deal with a team of medics with M6o's and Magnum ammo will know what I'm talking about).
I see it as a problem when people start picking medics for a reason other than healing.
2- Hording around objectives: Now I understand that maintaining a strong presence around objectives is important in both attacking and defending, but there's a difference between acting defensively and having the whole team camp in the objective room with all guns pointed at the entrances (namely one is an effective and fair stragagy requiring thought and planning while the other is just plainly being a dick for the sake of victory).
3- The lives system: Now I understand that attackers are given lives to make them be careful about their approach (although it should more logically be defenders who have lives, after all, attackers can easily bring more men in while defenders are limited to who is there at the time) but rather than just simply having it be 'game over' when the counter reads zero, how about simply making it 'no more respawns, you are the last man standing', this means that skilled and careful players aren't punished with defeat because their allies thought they were Rambo and ran face first into an emey MG. Also, giving the attackers lives means that when the counter runs low, many teams opt to just sit back in their base and snipe the defenders (who can't come close because of 'enemy mortar cover') until either the defenders rage quit or the attackers simply get bored and quit (while having defenders have lives means they can't use that excuse to sit back, they are compelled to get into the action because they have an objective to protect).
People like to slag off MW2 in favor of BC2 but in my experience they are just as bad as each other, they both trade off one flaw for another. MW2 has broken, cheap and overpowered weapons? So does BC2 (in the form of the M60 and M95). Oh but MW2 has cheap perks like stopping power, (then what do you call magnum ammo?) last/final stand (medics and their defrib) and painkiller/juggernaut (body armour?). Oh but Battlefield is more realistic (yet falling damage is pretty much nonexistant) and Modern Warfare has more variety (which the majority of players don't take advantage of).
I think the fans of both just need to grow up.