There are several D&D sub system from different editions I consider good mechanics.
The Swords & Wizardry Core Rulebook, I view this is the best minimal summary of the D&D game. It is an excellent foundation on which to build your own D&D.
First is Ascending Armor Class from 3.X is better than THAC0 or a chart look up in my opinion. This is coupled with a to hit bonus that increases as you level.
Rituals from 4e. I think for a referee who wants notch up the magic level in their campaign without turning the character into super heroes this is the way to go. At a turn casting time it doesn't impact combat much but allow many utility spells to be used during the course of the campaign. There is still some resource management involved if you rigorously keep track of the total components (in g.p.) that the player have on hand.
My Ability system from Majestic Wilderlands. Yes I wrote this so I am bit biased. But I really like how it works out in play. I may need to tweak the list at some point but so far it worked out very well. The main reason is that it been additive to the game rather than restrictive. The list and the bonuses show what the character are good at not at what they can't do. It is a fine distinction but an important one as I continue to run both of my Swords & Wizardry campaigns.
Unified Level chart. I think this is by far the more straightforward system of customizing a person's character I seen. Granted it takes a couple of levels to it's do it job but then in a skill based system if you spread yourself too thin and the character will suck at everything.
The problem with this is like feats in 3e and powers in 4e. You can just keep adding classes to the mix until the sun goes down. Which is why if this subsystem is used you should really look at the setting you are going to use and pick out the mix that reflects it.
I would use the Standard, Movement, Minor Action, Free Action system of organizing a combat round from 4e. Although the actual list of actions would reflect classic D&D more than later editions. I think this is a straight forward and easy way of organizing D&D combat. As for the dreaded Attack of Opportunity I would basically allow a free attack if the character with initiative tries to leave the immediate (5') area of his opponent his opponent using a full or half move. But if they just want to slide around in short little 5' move there is no attack of opportunity.
I would use the Spell and Magic Item selection from AD&D 1st edition. It broad but doesn't occupy endless volumes either.
I would tweak the monsters and classes to work with roughly the OD&D power range. When I first refereeing S&W I didn't really appreciate the difference with AD&D but I can see it now.
While there are more elements I would consider from various editions these comprised the ones I like the best and I feel will work well with the core rules of Classic D&D without adding undue complexity to the game.
In addition I am not making another clone game. I got enough on my plate at the moment. Mainly pointing out that there are good ideas in later editions of D&D.