This post is going to be somewhat stream of consciousness in nature. I'm going to look at each of the OD&D abilities and give my current thinking about each. Note that I say current thinking. I'm prepared to change my mind through reasoned argument, so here's chance to convince of how I've got it all wrong.
Open Locks: I actually don't have a big problem with this ability. It's an appropriate "specialist" ability and one that not all characters were assumed to have prior to the introduction of the thief class. Likewise, magic-users could already use knock to achieve a similar effect, so it's not alien to the milieu of early D&D.
Remove Traps: This is a bit more worrisome to me, insofar as previously all characters could theoretically remove traps. It is my understanding that the thief class owes its origin to players in the Greyhawk campaign who wanted to hire someone who was specially trained to deal with removing traps, which is is why I call the class "dungeon bomb specialists." I'm of two minds about this. On the one hand, why shouldn't there be someone trained in such things? On the other hand, why should such training be integral to only one class? I'd long used the Secondary Skills in AD&D and allowed characters with certain such skills to remove traps if I deemed it appropriate. Part of me wants to go back to a system like that, because the presence of a thief makes the other players lazy when it comes to dealing with traps and I don't want that.
Pick Pocket: I never had any problem with this ability, as it's specialized enough that very few non-thief characters have ever attempted to try it in my experience. Plus, it fits in nicely with the archetype.
Move Silently: This ability gives me pause, partly because I'm not quite sure what "move silently" is supposed to represent. Is it just the ability to sneak up on someone unawares -- and thus gain a greater likelihood of surprise -- or is it something more preternatural than that? Given that the thief is an archetypal "low magic" character class, I tend to favor the form interpretation, in which case I'd be inclined to give the thief a bonus to surprising an enemy and leave it at that. This gives him a clear niche without making other classes useless when it comes to laying ambushes, etc.
Hide in Shadows: Like Move Silently, I wonder what this ability is supposed to represent. Is it the ability to camouflage oneself so as not to be seen, provided it's dark enough? Or is another variant on being able to lay in ambush for someone? Part of me thinks this ability could easily be combined with Move Silently into a single one, but I'm not sure.
Hear Noise: Any possible objections I have to this ability -- which are few -- are overridden by the fact that, mechanically, this ability uses the same system as that for other character classes and that thieves are no better than elves, dwarves, or halflings till they reach level 3.
Climb Walls: I don't have a problem with this ability as described in Greyhawk, because it gives a system that's perfectly usable for other characters as well. A 1st-level thief has a 13% chance of slipping, with that chance decreasing by 1% per level attained thereafter.
Back Stab: Again, no real problem here. I'd allow any character, regardless of class, striking silently form behind a +4 bonus to hit. The additional damage bonus should probably be unique to the thief, or at least the increasing damage bonus should be. Must ponder.
Read Languages: I don't have any problem with a thief's ability to decipher treasure maps and ciphers, but I'm not so sure about reading dead or foreign languages. That just seems odd to me.
Read Magic: I know why this ability exists and I appreciate it, but I'm not sure it makes a lot of sense. I have many fond memories of thieves using scrolls at opportune times and of scrolls backfiring in amusing ways. Still, I'm not sure there's much warrant for this ability, particularly if one is reworking the class, as I am, to be more strongly archetypal and also more in keeping with the way other class abilities work. Must ponder this too.