What, having a 30% chance to climb walls at level 10 not good enough for you?
Surprisingly, climb walls is one of the few things where thieves have reasonable chance of success.
The 1e thief has a lot of problems. The biggest problems though are that you have a martial class that attacks using the same attack matrix as a 3e Wizard and gains no bonus attacks at higher levels and whose lacks any real defenses either in hit points or saving throws. The class is in fact front loaded. It never gets more powerful than the brief period between 1600 XP and 2000 XP where it has 2HD and decent saves, and then after that it is just straight up worse than every other class.
The truth is that 'backstab' is such a weak ability that even if they could backstab every round they'd still be doing less damage on average than a weapon specialized fighter of similar level.
The only balance they have against being worse than every other class in everything is the thief skills which at low levels are too unreliable to attempt and which at higher levels are completely outclassed by even the simplest spells - fly > spider climb > climb walls, clairvoyance > hear noise, invisibility > hide in shadows, find traps > detect traps, knock > open locks, etc. What you discover is that all you are doing is saving spellcasters spell slots but the amount of spell slots you are saving in a typical adventuring day is less than the number of slots you would have if you were a spell caster yourself, and then you'd also be a spell caster capable of solving other problems.
Worse, once 1e/2e started dabbling with a skill system in the form of NWPS, thieves weren't even the skill monkey as fighters got more NWPs than thieves did.
So at minimum to fix the thief:
a) They need to use the cleric attack matrix.
b) They need to get bonus attacks per round equal to a specialized fighter of half of their level.
c) They need to gain bonus damage with daggers at name level.
d) They need to advance Dexterity like a cavalier.
e) They need the most aggressive rate of acquiring NWPs.
f) Every time they gain a level, they should have the ability to advance an existing NWP as if they had taken it multiple times.
g) Their thief skills need to be overhauled so that they are more reliable at low levels.
h) If it isn't already clear, it should be made clear that they have the same dual wielding capabilities as rangers.
i) Their saving throws need to be reengineered such that they are clearly the best at saving throws depending on luck and reflexes.
j) Their XP advancement table needs to be reconfigured such that they tend to stay at least 1 HD above most classes and that gap increases as the things go on to at least 2 HD by 8th level (they hit 8 by the time most classes hit 6) and at least 3 HD by 16th level (they hit 16 by the time most classes hit 13).
And honestly, the class still wouldn't be that good but it would at least be playable.