DM Rolls Damage
This rule, found in the "Combat Sequence" chart on page B24, and under "Damage" on page B25, states flatly, "DM rolls damage" and "If an attack hits, the DM must determine how much damage the attack has done." The only time I have ever witnessed this is on the television show HarmonQuest. It's fine for players who are indifferent (or opposed) to rolling dice themselves, but the players I know love to roll dice especially if it's to generate damage against an enemy. Who am I to deprive them of their fun? I would ask why the rules specify that it's the DM's responsibility to make all the damage rolls, but I suspect it's derived from someone's personal play experience rather than a reflection of any standard practice at large.
Speaking of combat sequences, the aforementioned one on page B24 is complicated at first glance and ponderous in execution. I tried to give it a chance, but it instantly bogged down the game. A tense moment packed with potential excitement was reduced to a dull, monotonous litany of sections and subsections of discrete actions, and we were bored before we had even reached C. in the first round.
The only part of this rule that I can salvage is:
A. Each side rolls for initiative (1d6).
B. The side that wins the intiative acts first (if simultaneous all actions are performed by each side at the same time).
C. The side with the second highest initiative acts second, and so on.
D. The DM handles any surrenders, retreats, etc. as they occur.
Each side decides amongst its members who acts in what order and what action is taken. As a result, the game flows better and everyone is kept engaged in the action.
No Spells for 1st Level Clerics
Wrong. In my games, 1st level clerics automatically get cure light wounds. That's just how I roll.
Thiefly skills in B/X D&D, as with all editions of D&D, are mostly varying levels of gross incompetence until the thief reaches dizzying levels. A 15% chance to Open Locks; a 10% chance to Find/Remove Traps or Hide in Shadows? Why even bother with odds like that? I think I'd rather use ability checks (page B60, "There's always a chance.") or substitute the thief skills from Dungeon Crawl Classics RPG.
I use the AD&D class hit dice instead, but I let magic-users roll the same die as thieves (d6). In other words, fighter (d10), cleric (d8), thief (d6), magic-user (d6).
Other Rules to Lose
Other rules I'd lose or replace pertain to D&D in general such as alignment, level limits, and the overabundance of treasure and magic items. I'd also replace the level progression system with that used by DCC RPG or one of the "milestone" variants.
To reiterate, I admire the Basic/Expert rules more than any other edition of D&D, but no edition is perfect, and that's O.K. It's nothing a bit of tinkering can't fix.