I include a Thief class in my Swords & Wizardy campaign (though nobody has, as yet, chosen to be one) but I've never really found a decent mechanical means of reflecting their particular skill-set. At present, thiefly abilities are described rather vaguely and are heavily reliant on DM fiat.
In AD&D they were given level-based percentile chances for success at various things, like picking pockets or locks, or finding or disarming traps, or moving silently or hiding in shadows, or climbing things... I think that's about it, though I never played a Thief, so I never had the appropriate rules ground into my lizard-brain the way the rules for Fighters were. Anyway, that worked OK except that, by design or not, the fact that the Thief had these specific, delineated abilities tended to mean that it was assumed that other character classes specifically didn't have them. A wizard could never expect to successfully pick a pocket, because he wasn't a Thief.
That's significant, because in OD&D the implicit assumption was/is that any character can try anything, and success or failure depends enormously on circumstance (and how bastardly the DM is feeling).
One of the assumptions in OD&D is that, if in doubt, you roll a d6 to succeed in some task or other. Generally speaking, if you roll a 1 or 2, you succeed — whether it's jumping a crevasse, or throwing a line to a drowning comrade, or filching a purse from a passing fat merchant, or whatever... a character is assumed to have 1 chance in 3 of succeeding at any task that doesn't have an explicit success mechanism.
My thought about how to integrate the Thief's enhanced abilities without departing from the standard success mechanism (in other words, to make them better at things, not uniquely capable of attempting them) is simply to give them more chances to succeed.
Where another character rolls a d6 to spot a trap (succeeding on a 1), a first-level Thief would get to roll 2d6 and succeed if either of them showed a 1. Thieves would get additional dice for their thiefly abilities as they rise in level; I'm thinking at every third level (i.e. 3rd, 6th, 9th, 12th etc.), so a 7th-level Thief would be rolling 4d6 to detect a trap, and succeeds if any of them roll a 1. The higher the level of the Thief, the greater the chance of success, but there's still always a chance of failure — even a 30th-level Thief, rolling a whole handful of dice, might conceivably not roll any ones at all.
A corollary of this is that especially fiendish traps, difficult climbs, cunningly-hidden secret doors etc. could require more than one success to be achieved.
This mechanism would also be used for things like an Elf's enhanced chance to find secret doors — other characters have one chance in three of succeeding (rolling 1 or 2 on 1d6), while an elf has 2 chances in 3. Using this system, everybody succeeds on a 1 or 2, but the elf gets an additional die to roll.
I realise that this mechanism is not startlingly new or original; dice pools (I think that's what this is) have been used in lots of other games. I just think it would be a good fit for S&W/OD&D.