There are some links to youtube videos I had to remove. Instead, I put the title of each video so you can look them up in youtube yourself. Since when can we not use links anywyas?

3rd person
The community never asked for this. The lowest common denominator didn't even ask for this. I never asked for this. Firing weapons and generally doing anything from 3rd person doesn't feel anywhere near as satisfying or engaging as if it were done during first person. It's beyond me why the developers felt pressured to change a fundamental part of an otherwise good first person shooter:
POLICE STATION SHOOTOUT [HD]
Hopefully you'll come to the same conclusion upon watching this video.

And would Metroid Prime have been as successful as a 3rd person game?:
Gaming Mysteries: Metroid Prime Beta (Gamecube)

Melee
I found the melee system pretty satisfying until I realized how overpowered and blatantly uninspired a system it was. It's effectively an insta double death to any two targets within 3 meters. Combined with the fully upgraded cloak and batteries, it completely breaks the gameplay by making guns irrelevant. If it's about the fancy animations, games have proven that can be done better in first person:
Mirror's Edge All Disarms + Unused Hang Move
Riddick - Beating the crap out of people
killzone 3 brutal melee kills HD

Takedowns should be heavily regulated or removed in favor of the classic melee system from the previous games. Melee in real time in an FPS is highly engaging and rewarding. To pull off such melee requires skill and finesse, it doesn't cheaply freeze the action around you and insta kill your enemies.

Cover system
While in cover, detection and hit boxes for the player are drastically reduced to where you basically might as well be that flat bit on your side of the wall. To make up for this, enemy AI's detection and aiming speeds are ludicrously high. This means if you try to ignore the cover system when stealthing or while in a firefight, you'll be struggling a lot. On the highest difficulty, you can't afford to ignore the cover system in a firefight because you'll die instantly without your magic wall press. Even when leaning it seems you are much harder to hit while in cover. Ironically enough, even in cover I've encountered situations where the AI shoot me in the face barely before I can even technically shoot. This is no fault of mine, a single AI can and has taken me down by instantly headshotting when I've just barely peeked out, all by himself.
In future titles, the hit and detection boxes while in cover in addition to the detection and aiming capabilities of the AI should be at reasonable levels so as to make playing out of cover a less irrelevant option.
First person while in cover should also be an option:
Crysis 2 - Cover system

Boss battles
In DE1 boss battles were straight and to the point, often pretty short. This was justified by an exchange of dialogue that happened between the player and the boss before each fight. I see no reason for this to have changed, but there are other ways of drawing out boss battles that don't have to do with giving the bosses unfair and cheap methods to use against you such as invulnerability, ultra high HP, unavoidable attacks, etc. Instead make the boss play by the same rules you do, to elongate the battle make him stick to and utilize cover very efficiently, make him adept at avoiding attacks (not "magically" avoid attacks mind you). In other words, find better ways that aren't cheap and stupid in order to make better boss battles.

Setting and technology
In DE1, culture, setting, fashion and style are different enough, but not drastically so and therefore seemed to be a more feasible realistic future. Human Revolution's setting and style are totally unoriginal and draw cliches from science fiction, such as the awkard fashion. It's also stupidly bright orange. Human Revolution paints a future that looks totally alien, and it doesn't even take place as far in the future as DE1, which features older technologies like helicopters still being used.

Falling damage is too high.
If you fall just an inch above your jump height, you can take massive damage and die. This is obviously incredibly stupid, and should be changed for future games. You should at least be able to SURVIVE falling a distance twice your jump height.

The obnoxious anti-military sentiment.
Since when is the military bad for being the military? Like not bad because of some surrounding conspiracy, but bad by default? Really just bullshit. Yeah, the military needs weapons and still more powerful weapons to defend themselves and their countries. That's not inherently bad in itself. Hopefully that bullshit mentality was knocked out of Jensen's selfrighteous skull when he was thrown through that thick glass.

One other complaint while minor I hear alot is "Get rid of the slow fall animation or at least allow it to be turned off."

I'd like some boss battles to be solvable by dialog or stealth. I played stealth. And yes the melee system is overpowered, but I only realised this during the missing link DLC. Until that point I wasn't aware of the fact that you'd always regenerate back to 1 energy level, so I spent most of the time just avoiding enemies rather than taking them down because I wanted to conserve my food. And then I had to keep my inventory full of weapons for when next I got into a boss fight.

As for the 3rd person gripe. Wasn't it only third person when you were in cover? Your gripe made me wonder if I just remembered it wrong, but no...looking over screenshots I'd taken it's very much first person except when you cling to walls.

Only gripe I have is boss battles, i hate them and always have. The game played great in many different ways I have no reason to complain. It was alot better then the money I wasted on the original all those years ago.

Augmentations need to be way more difficult to obtain. I think I finished the game with like ~10 locked augmentations (with the DLC, but still).

Other than the boss parts, I had no issues with these 'problems.'

Going to echo the majority of the thread so far; the only things I'd change are the boss battles and maybe a true melee system (as in not insta-kill or sleep) based on the weapon you're using.

I absolutely loved the rest of the game and I personally find it a much more satisfying game to play than the original Deus Ex.

Tbh, and I may take some flak for this, I very much enjoyed the accessibility in DE: HR. I don't think it was as bad as DA: 2's "awesome button," but it did make the game simple to pick up and play.

I actually enjoyed the atmosphere for the most part, as it was hyper-reminiscent of Blade Runner, and due to lack of new Blade Runner material out there, I took to the setting quite well. That being said, if they make another DE, I'd want a bigger, less linear world and a little more open exploration, etc.

I do agree that having proper dialogue options to find your way around certain problems would add a new element to the difficulties you face, but I don't think not having it for the boss battles was that big of a deal.

I also REALLY enjoyed the soundtrack and listen to certain tracks pretty often. The big thing for me is how immersive an experience is, not how much it clings to everyone's ideas of how it should be more true to the first game.

For me, personally, there really wasn't an immersion breaking moment for me. I do think some of the side missions had a little more depth than simple fetch quests, but at least they attempted to add a little flavor and variety to them.

All in all, sure, Human Revolution may have a few things that make it meme-worthy, such as the repetitive "I NEVER ASKED FOR THIS" jargon, but I don't regret the experience of playing it. In fact, I very much enjoyed it despite its "issues."

For what it was, I too have enjoyed Human Revolution. The biggest issue I've had with it was the story, which completely captivated me in the first game and I found it terribly boring in the HR. As story is one of the most important factors about gaming as far as I'm concerned ... Yeah. And the utterly terrible switching of 1st and 3rd person modes. It'd be fine if the game just sticked to one, be it 1st or 3rd, but nooo - I found it terribly counter-immersive.

While I would very (VERY!) much enjoy a new DX that was basically a renewed version of the original, just with better graphics and smoothing the clunky parts, I think DX:HR was pretty decent on it's own. Like most pople above, I found the bigger problem to have a stealth-based build and then suddenly be placed in front of a humanoid tank without warning, and giving you nothing but direct assault as options to deal with it.

I didn't like the hacking minigame, but I generally hate every minigame that you have to keep doing (like the lockpicks on TES or the like) and that's a subjective thing. I didn't like the way they balanced the builds and provided experience by making few combat based augmentations and then giving you less experience for going guns blazing. And the takedown animations with their time stop were just stupid. This said, I don't believe these are things to be "fixed", just traits of a game that I actually enjoyed quite a bit.

Repetitive takedown animations - some variety wouldn't hurt; and they were clunky as hell. Didn't like voiceacting at all especially concerning Jensen.

Personally my main gripes about Deus Ex HR (you already mentioned some) :

Takedowns :

They are ridiculous, overpowered, immersion breaking : make a tiny noise and everybody will hear you from the other side of the room, but punch a guy repeatedly in the face, break his arm and finally snap his neck and magically you are invisible and don't emit any noise and the other guard 1m away won't hear nor notice anything.

Dishonored handled lethal/non-lethal take downs that much better, it didn't break the immersion, there was a risk of being noticed involved, etc...

AI Improvement:

That's a tricky one as AI will always be "unrealistic" and very few games manage to do it correctly; but still you expect humans to have ~180 degrees field of view... not 40 degrees like they have in DXHR and if two guard are talking together, you expect, if you get rid of one, to have the other at least wonder why the guy he was currently talking to suddenly disappear into thin air.

Level Design :

Having multiple alternate paths is a good thing... as long as they are not ultra obvious with a blinking "the alternate path is right here you moron! red sign on top of it.

I was unable to keep my suspension of disbelief for more that 2-3 minutes in DXHR, sometime that was ridiculous : a long empty corridor, an empty cardboard box in the middle.... and guess what ? a ventilation shaft right behind it, ventilation shaft that just happens to lead you where you need to go... talk about a strange coincidence...especially when it's the 20th times in a row...

Once again I find that Dishonored, while not perfect by any means, managed much better to give the illusion of "realistic" alternate paths.

Upgrades :

I found most of the upgrades to be pretty bland, most were the kind of upgrade you can expect to find in CoD or similar other recent shooter, I was expecting more "cyborgish" technologies; I mean you are a cyborg after all, I was expecting to be able to customize my leg and arms, have more "distinctive" upgrade path, etc...

Boss battles and the 3-button room aside, I loved everything about it.

I was skeptical at first about the 3rd person cover system, but within minutes of playing, I thought it worked really well.

Although I loved the takedowns, I'll admit that I do miss having melee weapons. The prod, the baton, the energy sword, pepper spray...

The two biggest ones for me is that 3rd person should have been completely optional, and takedowns (seeing they break immersion and gameplay) should be replaced by more traditional melee, or at least like what we've seen in Mirror's edge.