D&D's wonky game mechanics never used to bug me. Low AC was good, high HP was good, roll high on a d20 to attack, roll low on a d20 for an attribute check - I had no trouble grasping it all, and never gave it too much thought. When I started playing 3.5 it took me a second to get used to the new concepts, but that too came swiftly. Recently, however, I have introduced my girlfriend and a host of other first time pen and paper RPGers to Mutant Future in my ongoing campaign.
Mutant Future is a relatively rules light game, due to its Labyrinth Lord cum B/X D&D heritage, but it has been difficult to get everyone to remember the rules. While there are not a lot of rules in terms of specific game mechanics to govern things like the use of skills, or sneaking around, or any of the other things that have been codified in 3.5 and 4e, what rules there are have little mechanical relationship to each other. People ask me constantly if they are trying to roll high or low on a particular throw of the dice, because they like to know before they throw. I remember one attribute check when somebody rolled a natural 20 and was very excited until I told them it was the worst thing they could have rolled.
I have also been asked the difficult question, "So why is a lower AC better?" and have given my dutiful old school answers, that it stemmed from a miniature war game, that descending AC lets you add all the modifiers on both sides of the attack roll together, that it is just the way it is, dammit!, but it still seems dissatisfying to the players.
What I have come to realize is that there really isn't any good reason (in my opinion) that all the mechanics in a game shouldn't share some logical principle that makes them easy to explain to a first time player. While I am not a big fan of 3rd edition D&D by any means (4e I like for its tactical combat options), this is something that I think it got right. This may hurt my old school credentials, but then again, I'm not even 30 yet (barely) and I started playing D&D with 2d edition.
Being able to tell someone, "The basic mechanic is that you add your modifiers to a d20 roll and try to match or beat a target number" is much easier than having to explain all the ins and outs of the old school method.
Just my two cents worth.