Abstract short and long rest. I am particularly not fond of regaining all your hit points over a long rest.
- The lack of meaningful long term status conditions like poisons, diseases, and curses.
- Martial abilities with arbitrary resource management without any direct correspondence to the fiction. Stuff like superiority dice, rages per day, bardic inspiration, second wind, and action surge.
- Hit Dice/ Healing Surges. Particularly when healing does not use them up they do not really feel like extra reserves.
- Ability Score substitution effects like using Dexterity for attack and damage on finesse weapons or the Hexblade's Charisma to Attack and Damage. Also stuff like the Barbarian's Constitution to AC that lets them run around naked.
- Monsters that lack meaningful resistances, weaknesses, and immunities.
- Monsters with incredibly bloated hit points when compared to PCs
Well, I'm not sure if 'agree' or 'disagree' is the right term. I don't think anything in 4e is cast in stone as the 'right' way to do it...
1. Long rest in 4e practice and in HoML is simply a break point. It could come after a day, a certain plot point, etc. I would point out that making it a day is in keeping with the 4e theory of putting control more in the hands of the players, or at least giving them a degree of certainty and non-arbitrary parameters to work with.
2. I don't have a problem with 'abstract' resources. If you boil a 4e game down to a narrative then it easily works out to be basically "sometimes each character manages to be special" and the exact mechanical instantiation of that at a given instant in time is relatively unimportant. A fighter making a 'big move' could be simply expending a daily in an advantageous way and getting a crit, or it could be a Standard -> daily -> AP -> daily -> minor action attack combo, or burning an item power, or some feat effect kicking in, and/or any combination of the above. Its not really all that important which mechanics were engaged. The mechanics are there to give structure to the player's choices and make it a GAME and not a story-telling exercise.
3. I took my game in the direction of less specific resources, Vitality Points are a much more universal currency. I have this feeling you're a bit hung up on 'flavor' here.
4. I have no idea why you don't like DEX being an attack stat for weapons where it seems appropriate. Why is STR somehow sacrosanct as the only realistic option? I don't agree with you at all on that point. The other forms of substitution I think are possibly a bit more 'hackish' in the sense that they were implemented to provide players with a way to bypass hard choices in character build, which I don't really agree with. In terms of logic however, I see no reason why a wizard's hit points shouldn't depend on INT, most hit points are a reflection of intangible forces like 'luck' or at least of 'skill' anyway, why is CON the only thing which can grant this? You seem to just have become hung up on tradition in some cases here.
5. 4e DOES have monster 'weaknesses', but they're not as absolute and simplistically implemented as in other editions. This means they don't form hard blockers and force certain PCs totally to the sidelines such as happens in 3e or (maybe to a lesser degree, I'm not sure) in 5e.
6. Monster hit points simply represent a slightly different thing than PC hit points in 4e. Think of it as a simplification if you wish. Monsters have hit points and 'surges', but it is all just rolled into one for the sake of playability. Try PvP play sometime and you will see why this is really by far the most workable solution.