Many good suggestions in here so far, Eridanis. What kind of game are you planning to run?---that'll help with more-tailored suggestions, I'm sure.
In general, I've found that the more I've tinkered with combat rules, the less happy I've been with the results. The OSRIC rules and DMPrata's ADDICT doc are really good summaries of how to play 1e combat without the parts most folks ignored (weapons vs. AC, weapon speed, etc.). FWIW, at low-levels, weapons vs. AC actually are pretty helpful (i.e., increase the chances of PC survival to mid-levels), and if you use the Combat Computer from Dragon 74 they're very easy to integrate into the game (I've use them while DMing since Dragon 74!).
I've also used several of Tewiligan's rules in the past, but have stopped using some since BITD:
1)
M-U's get bonus spells for high INT, using the cleric's chart for high WIS. - I used to do this, but stopped: MUs are far too powerful if they get bonus spells; I also use the INT rules for spell acquisition and min/max # of spells per level known, as well as the BTB spell acquisition process (you can a spell of level X in your spellbook when you gain a level and your number of castable spells per day goes up in that level)
2)
Max HP at first level. - I've always done this.
Afterwards, players can either take half the max roll when they gain a level, or take their chance with the dice. - I have players roll all levels after first, and what they roll is what they get. PCs also record the HP die roll, for when they're energy drained.
3)
Thieves use the more flexible thieving skills allocation from 2e. - I haven't seen/used this, can't comment
4)
No Unearthed Arcana classes or races. However, demihumans from the PHB do use the more relaxed permitted classes/level charts from UA. - From UA, I allow barbarians (but based on the Dragon 63 original moreso than UA) and cavaliers (though not elven), as well as the heirophant druids, and most new spells/magic items; I no longer allow PC drow/duergar/svirfneblin races in campaigns, but have in the past in evil and/or underdark campaigns. I have my own charts for racial level limits and multi-class options, but the UA ones are fine-ish. I also use the UA errata published in Dragon 103.
5)
Unconscious at 0 hp, dead at -10. - Yep.
6)
Clerics can swap memorized spells for the Cure spell of the same level. - I make clerics memorize all spells, including healing spells. With High WIS bonus spells, this hasn't been an issue for me.
I'm back and forth on weapon specialization: if you allow only single-classed fighters to have it, I don't find it to be that unbalancing; if you allow multi-class fighters to have it, then it gets way too powerful. Also, weapon specialization is only really relevant if you use weapon proficiency, and non-proficiency "to hit" penalties; if you don't, then I definitely wouldn't allow specialization.