What the heck is "compatibility"?
Do you expect a player that "I know how to play D&D edition X" to sit at a gaming table playing edition Y and be able to play using rules X? Not going to happen.
Do you expect someone to bring a character sheet written for edition X and play that character in a game of edition Y? Not going to happen.
Do you expect the DM to pick an old adventure written for edition X and play it as-is in a game using edition Y rules? Not going to happen.
Do you expect the DM to pick a monster from a book published for edition X and put in into an edition Y adventure? Not going to happen.
Nothing like this has ever happened, because each edition has its own numbers, mechanics and other rules. Different editions have different math, so that combat stats scaled differently; when only numbers differ, you might be able to use a character or monster in another edition, but at the very least you need to know how to compare it with others (e.g. a level A character/monster of edition X is not going to be still a level A character/monster if dropped into edition Y, at the very least you need to know what its new level B is). Some mechanics exist only in some edition, in which case some stuff simply doesn't apply.
Then even if you take two very close versions of the game such as 3.0 and 3.5, you may drop a 3.0 PC into a 3.5 game or viceversa, but you have a secondary problem of fairness, because the 3.0 character is going to have something less than what it would have if created with the 3.5 rules in the first place.
So if you mean compatibility as "no need for adjustments", you're failing before starting, because previous editions are already incompatible with each other. Thus how can 5e be compatible with OD&D, AD&D, 3e and 5e if none of them is compatible with each other?
The bottom line is, if you want to use an adventure, character or monster from a different edition, you should always be expected to adjust it. We can discuss how much adjustment is tolerable, or how to design 5e to make necessary adjustments less, and then talk about "compatibility" in loose terms, but not more than this.
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A very different thing from compatibility is replicating the gamestyle.
Rules determine gamestyle, and even numbers ranges influence it.
To play a Vancian spellcaster in old editions, where you really had your few daily slots and not much more, has already a significantly different feel compared to play it in 3e where (if you don't diverge from the wealth-by-level tables) you have easy access to scrolls and wands, and it's going to be different again in 5e with cantrips at-will and rituals. 4e is even more different because of the AEDU system.
5e took a very bold design target of being inclusive of gamestyles, by presenting ways to create characters tailored to different gamestyles, but it's very hard design, and in fact you won't get the feeling of a spellcaster of any of the previous editions as a result (mostly because of the presence of cantrips and rituals as a default, instead of as an option).
At least the inclusiveness has a lot of merit. Because if you want to really get the feel of BECMI or 3e, you should go and play them, not play 5e, and at least WotC is now providing many old edition books for sale in digital format. But you are on your own finding enough people who want to play the same thing as you. If you have such people already then great, why are you even complaining about 5e not giving you more? You already have what you need, you should be happy. OTOH there are also people who are not that lucky, and maybe 5e can give a help bringing back a group together, where one player wants a PC that is simple and relaxing to play, another wants to tailor fiddly bits around it, another likes daily-based resource management and the last one cannot stand it at all. But they still have to make the effort of seeing these "gamestyles" in more general terms, not focusing too much on the mechanics.