For whatever reason, I will try to put together some house rules and issues from back in the day, in no particular order:
1) Clerics and Priests: really three things--clerics know too many spells, specialty priests seem like a cool idea, and clerics have utility spells that can impact play, if only they were prepared in the first place. My solution, limit the number of--spheres, I think--but allow what would later be called spontaneous casting. Also allow druids to have spontaneous casting. Also, for specialty priest, don't be afraid to give them a few cool things on top of their spells. (yet another alternative is to allow all casters spontaneous casting, but not be able to cast the same spell more then 1 time per day. yet yet another is to do a ritual type thing, and cast from a spell book or through prayer at an increased casting cost in time or gold).
2) Running out of spells: long before at will magic, we worried about this. In hindsight, AD&D addresses this through wands and other items. Which is a good solution, you can increase flexibility quite a bit, keep things under (DM) control, but there is still a trade off in charges. If this is not enough, you can maybe allow some kind of over casting, ie cast an unprepared spell and lose 1d4 con for a day.
3) whimpy thieves and skill users: some people love the thief archetype, otherwise no one would have bothered to play one. I suggest giving a boost on % chance of success for easier (ie low level) tasks of at least 20%. Rangers and other % skill users can also benefit from this. Also, be generous with backstab. Let it happen. (also see 10 below)
4) multi and dual classing: let non-humans dual class and humans multi class. Its fine.
5) non-human level limits: We used an XP penalty (double I think) instead and I still had plenty of non-humans. What I might do know is let humans add +1 to any ability (up to 18) and maybe give a 10% XP bonus, and again remove the limits.
6) They die so fast: in the past, max HP at level 1, fudging some roles, and a generous death door policy. Though just giving +10 HP would be simpler, but maybe no purist enough. For save or die, maybe interpret die as "0 hp" (but still allow save or stone, charmed, etc, etc)
7) THACO...ugh. Use those sheets were they fill in a little thing were they see what AC they hit...
8) Fighting fun: weapon specialization is good, use it, and maybe allow others besides fighters to give up WP slots for it (not sure what the RAW was...maybe fighters the only ones at level 1?). We tried various maneuver rules. I might allow a called shot rule (-4 to hit to do something interesting) if it was clearly not being abused.
9) kits: I liked them, I hated them...but some of them were alright. This is were the OGL/OSR crowd could do something useful, not sure they have.
10) really pushing it...replace roll under NWP with a % based skill system. Maybe use some existing NWPs and skill or skill like things and then have a standard set of %s based on ability score and or level.