So here are the rules: present a "problem" with D&D (any edition will do) and explain why you feel it is a problem (this part is really important) and the either suggest a fix, or ask for a fix from fellow community members.
Ooh, I've got a bunch of these for 0e.
THAC0: In my experience, the best way to figure attack rolls smoothly and quickly in old-school D&D is to leave the descending AC value alone, but subtract the character's THAC0 from 21 to turn it into an attack bonus, and then
roll low to hit. That is, you find the target number you need to hit by adding the target's AC and the attacker's to-hit bonus, and you want to roll that number or less. A 4th level fighter (THAC0 17 → +4 to hit) rolling to hit a target in mail armor (AC 5) has a 9-in-20 chance to hit. It's easy-peasy, and it ensures that you're always dealing with low numbers (it's nearly always single-digit addition, in fact, which for most players is going to involve the fewest mental blocks and the quickest in-your-head calculations).
Abilities & Skills: This one sort of kills two birds with one stone. In old-school D&D, there are lots of mechanics (opening doors, surprising enemies, locating traps and secret doors, hearing noise) that handled with a simple roll of 1d6, and depending on the circumstances, characters have an X-in-6 chance to succeed at the task. With the exception of opening doors (which is modified by Strength), these task-resolution rolls don't interact with the characters' ability scores in any way, although they do sometimes overlap with thieving skills. Well a long time ago, I decided to lean into this and created a skill system based on d6 rolls to entirely replace both thieving skills and all of the various d6-based mechanics in the game (as well as the D&D "general skills"/AD&D "non-weapon proficiencies" systems that I've never been particularly fond of).
How it works, in brief, is that there are 12 skills (Athletics, Civics, Craft, Diplomacy, Entertain, Knowledge, Medicine, Outdoors, Perception, Pilot, Stealth, Trade), and all characters start out with a 1-in-6 chance to pass any skill check. They can buy additional skill ranks to improve their rolls with skill points (most classes get 4 points at 1st level and extra points on odd-numbered levels; rogues start with 6 and get one point per level). Very simple, very straightforward, and it provides just enough customization that players can differentiate Bob the Fighter, who used to be a blacksmith (Craft and Trade ranks) from Fred the Fighter, who used to be a woodsman (Outdoors, Perception, and Stealth ranks).
I also found that by having this skill system in the game, it completely removed any need for raw ability checks, of the old roll-under-the-score-on-1d20 variety. If you don't use a system like general skills or non-weapon proficiencies, ability checks are totally optional in old-school D&D anyhow, and without them the ability scores themselves don't carry that much mechanical "weight." (This is good for a couple of reasons: it makes rolling your scores on 3d6 in order a tenable prospect; and it does away with the notion that a character with Dex 8 and a character with Dex 13, both rather average scores, have a 25% difference in their respective chances to pass a "Dex check," which is frankly terrible game design and not part of the original D&D rules for good reason.) In fact, I found that I could bring the ability scores all the way back to where they are in the white box: they serve as nothing more than prime requisites for the character classes, adjusting earned Experience Points as their main function (with ability score modifiers being a very minor, very secondary function of the scores).
From there, it becomes possible to go even further—to characterize the ability scores as pure abstractions rather than totalizing descriptions of character ability. The Strength stat doesn't literally represent the character's muscle and physical prowess (I have the Athletics skill doing that in my game already); it represents a character's innate
fighteryness. The Intelligence score isn't the character's education or thinking and reasoning (education is handled by skills like Knowledge and Medicine; meanwhile, the
player brings the thinking and reasoning). Instead, the Int score is just the character's natural
mageyness. And so forth. Sometimes, to drive this home, I'll even rename the scores entirely. (In a 1920s pulp game I'm starting soon, I've renamed Strength to "Guts," Charisma to "Moxie," and so forth.)
The end result is, perhaps, an utterly foreign way to look at the ability scores as far as most D&D players are concerned. But for me, that's just another thing to like about it. It's
different—in a way, it almost makes the game "mysterious" again, even to players who are otherwise old pros.
Encumbrance: Tracking encumbrance by weight is tedious, no matter whether you use the old D&D coinweights, or you switch to pounds or kilograms or stone. But I can't stand true slot systems either: any encumbrance system where you just count items (and OSR games are
full of these) strikes me as intolerably abstract. So I settled on a hybrid weight–slot system. It actually works pretty well. Basically, I put 48 cells or slots on the character sheet, divided into four blocks of 12 cells each. (Here's an
example from my upcoming pulp game.) Each cell can hold 1 kg of gear, so you could put a couple of daggers or 100 coins in one cell, but a sword would fill two cells. Every full block of 12 cells shifts the character into the next encumbrance tier (from MV 120' per turn down to 90', then 60', then 30').
The advantage to this system is that you never need to tally up item weights to know how encumbered you are: instead, you just glance at the sheet and see whether you've met a certain threshold or not. No need for the players to track every pound, but also no chance that That Guy will ever mysteriously undercount his carried load!