QTEs I'd like to see done more organically TBH. I mean, everything they're used for is something that could be done more organically, but is locked to a specific sequence for god knows what reason. I.E: Fighting some guy in an FPS hand to hand. Being told "Press E, left click, right click, space, ect." is kinda boring, and isn't very involving. I had the same sort of thing in FC3 when you were attacked by an alligator or something and had to press a random button a number of times to kill it. If you got into the fight and weren't necessarily given instructions, but could press left mouse button to attack, right mouse to block and E for a situational attack [I.E: Slamming a door on someone], I wouldn't mind as much. Give the player instructions the first time, but after that you attack when you want to attack and defend when you want to defend. Of course the whole thing would still be largely scripted so that it looks as awesome as a cutscene, but instead of not pressing X leading to your death, you can press left mouse and attack them, starting a brief combo of hits, or right mouse to block them, starting a quick counter to their attack. Multiple stages of each fight, multiple options for each stage, and a few combos of options that lead you to victory, and are actually intuitive button presses as they have a purpose rather than random button presses to present a fake challenge.
QTEs do need to only appear where necessary though. No bloody rats biting your finger and killing you for no reason.
Button mashing is really a part of a quick time event, just one you can't always fail. I don't mind these most of the time, but there are times when they are included and don't need to be, or are just waaaay too long for what they are.
Regenerating Health I also hate. I think Halo got it right - the Original one. Shields regen, health doth not. You had a minimum level of health you'd be on so any encounter was still possible, removing the 1 health no options problem, but you also were continually disadvantaged for losing too much health, and you couldn't just run up, take out three guys by the skin of your neck with 1hp left, and then be left with no consequence for your risky action because all your health just re-appeared because a wizard did it. Additionally I'd like to see it coupled with more movement based mechanics like old school games, rather than the twitch mechanics of newer ones.
Another thing that I dislike; Bullet exchanging magazines. Got 12 bullets left in this magazine? Don't worry, reload now and those 12 bullets are just transferred to another magazine. I liked it in games like Battlefield 2 where you'd have a limited number of magazines, and an amount of ammo per magazine, rather than just limited ammo. You had to decide whether it was necessary to reload or not, as reload times were reasonably long, and if you ran out of bullets in a fight you'd be dead for sure, but at the same time reloading when you had only used half your mag would lose you the other half - it wouldn't just get added to your average ammo count, you discarded that mag and all the ammo left in it. More to think about and manage, and more gameplay choices you had to make that I enjoyed.
Additionally FoV needs to be increased to a 100' minimum for all games, preferably 110'-120', and at the very least there should be a slider with such options on it. 90' or less FoV is just annoying.
Quick kill twitch mechanics also need to die in a hole. I don't want to die in 4 bullets from a gun that shoots 2.5 bullets per second. I want to die in 8 bullets from a gun that shoots 1.5 bullets per second that actually travel rather than just hitscan, or in 2 bullets from a gun that shoots a bullet every 5 seconds or so, and isn't obsessively long range so only another person with such a gun stands a chance of eliminating the player. I'd also like to be able to dodge bullets by movement and in general just go back to old school shooter days. They were more fun. Went to a gaming night a few days back. CoD and such was available. We didn't play that, its not fun. We played the original Halo and Quake 3 and Unreal Tournament. There's more you can enjoy from it, and you can actually appreciate skill in it as opposed to "Oh, you saw me first. Oh well."