Jeff Rients is asking what the most annoying rule or subsystem in AD&D is. He offers a short list, all of which I find annoying to one extent or another, but I thought I'd comment in detail here, instead of there.
Demi-human Level Limits: Actually, not all that annoying. Same goes for demi-human class restrictions, which weren't listed, but are related (think of a ban on dwarf clerics as a level limit of 0.) I'm more annoyed by the term "demi-human" than the level limits. Still, it's a restriction I'm willing to lift; I think I'd just treat advancement beyond the level limit as changing classes (in other words, you need a 16+ in the prime ability and may need to do some specific questing.)
Weapon Speed: The basic idea isn't too bad, but I don't like the implementation. A crude guesstimate based on length is enough for me; looking up numbers and applying them to segment calculations is annoying. But that leads into...
Initiative: Discovered I don't need it. The original books don't mention initiative or anything like it. The side with the benefit of surprise gets to go first; otherwise, ask the players what they are doing first, determine the actual order of actions based on crude weapon length; Dex is a tie-breaker. If other actions are involved, use Dex to determine order. Much simpler than the fiddly AD&D initiative system.
Weapon vs AC: Used it a few times, found it annoying, dropped it. But I'm toying with a much simpler system, so it's not the basic concept, just the implementation as a bunch of numbers arranged in a table.
Material Components: Do magic-users really need to be more limited than they are in Men & Magic? It's like people are still afraid of magic, even in a made-up game. Again, additional look-up time involved in spell components (or casting times, or many other spell stats) just annoy me. I'd rather have material components as a way to expand standard spells, instead of as a requirement. So, adding powdered goblin heart when casting Monster Summoning I lets you specifically summon goblins instead of some random 1st level monster.
Psionics: It's the annoying subsystem: extra numbers to track, unique attack resolution that slows play and removes the participation of the non-psionics. Same applies to the grappling rules or the non-lethal combat rules. Why not just use the standard combat system with a couple adjustments?
Training to Level Up: Not a big deal, but it doesn't jibe with my interpretation of "level' as a combination of reputation and general experience. And honestly, I don't need a method of extracting more money from player characters; the 1% maintenance tax is more than enough.
What I find most annoying about AD&D is the minimum and maximum ability scores. Actually, pretty much anything to do with the way AD&D handles ability scores. But that's probably best reserved for another post.