Hmmm...rebuilding 1ED? Making it stronger, faster, better?
Yes, but I would think retain core 1st edition traits. In particular, we have to avoid the temptation to answer the question with a fixed version of 3rd edition (which I would love to have as well, but that's a different subject).
1) Keep classes, but use something closer to the 3.XEd multiclassing rules. To keep more 1Ed flavor, Humans would use standard 3.X multiclassing (but with primary stat score minimum requirements), non-humans would use Gestalt rules for multiclassing. While this doesn't sound like much, if nothing else, it opens up a variety of multiclassing options for non-Elves.
The Gestalt multiclass-ing for demihumans is I think absolutely key to 1st edition flavor. Third edition multiclassing for humans is tempting as a replacement for the dual classing rules, but I think it would mean things like dropping the combat/to hit tables and wierd things with XP advancement that would make the game far more like 3rd edition than 1st.
2) No level caps or multiclassing penalties for any race.
Why? I keep seeing lots of requests for this, but I don't see the need of it. First edition style games don't go to level 20 by default. It's a rather third edition mindset involved here I think. Frankly, all that is needed is to rebalance demihumans with humans enough that the level caps for demihumans are near to the high end of the expected range of play. So, for example, it might be nice if halfling fighters didn't top out at 5th level, but 8th or 10th is not an unreasonable level cap.
3) Use the 3.X "higher is better" standard for all rolls and AC. IME, AC going negative as a good thing was often confusing for new or casual gamers.
There seems to be general agreement with this, or if not, then at least no strong disagreement.
4) Unify all of the stats, a la 3.X. The different treatment of Str for warrior types was another stumbling point for teaching the game to new players.
I agree with the concept, but not the reasoning. The problem with the different treatment of strength is that it required special exceptions all throughout the rules for dealing with it. However, I think its important to note that the different treatment of strength is one of the fighters core class abilities. So, if do away with it, we have to do one of the following to maintain balance:
1) Double or otherwise the strength bonus fighters get in combat (this gets out of hand though when the fighters get high level magical enhancement).
2) Give the fighters a reoccuring strength boost to simulate that higher strength that they've now lost.
I advocate for #2.
5) Use 4Ed-style unification of class level and power/spell level: 1st Lvl Wizards get 1st lvl spells, 2nd level Wizards get 2nd level spells, etc. This would require the re-leveling of certain spells.
Again, the original form was confusing for too many people.
No. Again, I find this very justification very hard to believe. I never encountered it in all my time playing, and moreover the D&D spell level system was wholesale adopted throughout the computer RPG industry. It's widely familiar and (much like hit points) via the cRPG industry throughly tested as a legitimate mechanic. I'm not convinced that in the context of 1e your proposed fix wouldn't even be more confusing. I "2nd level Wizards get 2nd level spells", then I foresee new players being confused that they can't use all of thier spell slots for 2nd level spells.
6) Like the Thief skills, all skills use % system to determine success or failure...but the PC's % shouldn't just be a pure chance of success. There should be a chance for targets of those skills to thwart PC successes, a reflection of THEIR skill and experience. Perhaps something along the line of the skills system of games like the original Stormbringer (1981).
I believe a truly generic skill system would get in the way of 1e's focus on player skill over character skill. Skills should be reserved for exceptional abilities. Skill contests and the like should be informal, and really all that is needed is some guidance to the DM in the DMG on how to resolve non-combat contests.
7) Integrate psionics into the game, at least at the mechanical level. 2Ed and especially 3Ed did a good job of making the psionic powers mechanically similar to spells by Wizards & Clerics.
No no no no no no no. That's exactly what you don't want to do. First edition had by far the most flavorful and interesting Psionic system precisely because it didn't do this at all. If you are going to make psionics mechanically similar to spells, then you should drop them entirely and simply say that practioners of psionics are simply members of one particular school of wizardry. Spell like ESP, clairvoyance, and the like are already available for this purpose.
Make the Bard into a normal base class instead of what is, essentially, the first PrCl in D&D.
I continued to play 1e long after the introduction of 2e, but we did adopt the 2e Bard.
9) Reduce the number of classes, but give more options within a class- kind of like a cafeteria of options...a silo of related abilities- which would let you simultaneously customize your PC and define his or her role.
This is not the 1e way. First edition is for better or worse an entirely class centric game. Being 'player skill over character' and being able to define a character almost entirely by class and level are central to maintaining the advantages of 1e play. If you start making 1e classes more like 3e classes, then you pick up both the advantages
and disadvantages of that. For one thing, you can no longer stat out an NPC simply by writing 'F5'. Simplified stat blocks are one of the major attractions of 1e, and you risk throwing it all away.
The classes needed, IMHO, would be Rogue, Spellcaster, and Warrior.
And now you are murdering a sacred cow or at the least unnecessarily complicating the whole concept of subclasses in a whole bunch of ways I don't think you are really thinking through.