Regarding the blind spot: I'm not sure it's really an interesting element. After the undead snipe at the PCs from the arrow slits, any PCs who want to avoid targeting will probably just hide up the western stairwell. Sure, yeah, maybe using an in-the-room blind spot will serve some narrow tactical purpose, but I'm not convinced it's worth explicit words. The blind spot is already evident from the map itself, given the angle of the arrow slits themselves. In fact the northwest corner of the room probably counts as another blind spot.
Is the large shield a possibility space? Where I come from, most fighter types carry a large shield already. it doesn't give +4 AC though, it only gives +1 AC vs 3 attacks/round. +4 AC is a massive bonus in old school D&D — in AD&D it's about as big a bonus as you can get, analogous to the defender being invisible, or having 50% hard/impenetrable cover. This shield is probably more like a portable barricade, or maybe a tower shield (if the game supports it). Why not just leverage the game's default mechanics, and trust the referee to intuit the amount of cover or other good mechanics? You could still say, "a cracked tower shield (shatters after 5 attacks)." (And I picked "attacks" intentionally instead of "hits.")
Rusty hinges aren't a possibility space. It's just a standard stuck door, with rustiness as in-world color.
The pit: The depth is absolutely important to know; that's the first thing a player would ask about when they fall in. Every old school version of D&D already has rules for damage for falls of varying heights. As the reader, I have no idea what you intend here. Is it supposed to be merely an inconvenient 5 ft pit that PCs can easily scramble out of? Or is this supposed to be a 10 ft pit that will cause falling damage, then takes help, gear, or special training (thief abilities) to escape? It's fine to let the referee just make up the answer, but it's also an omission that makes the designer look like they accidentally forgot a detail.
On monster stats, don't list more than you think you need. Anything else potentially gets in the way, unless it's a big convenience. There are not always absolute answers on how many stats to list, but a tiny bonus in very narrow circumstances is probably not worth listing. For those undead brigands specifically, as referee I need to know what type of undead they are (skeletons, zombies, something else?) for purposes of turn undead. I don't need to know how they save, because 1 HD already tells me how they save for all old school versions of D&D.
What I like: The general concept of a series of rooms where monsters take advantage of sniper positions as PCs move through the complex. But I think you can communicate that better, especially since rooms 3 and 5 also appear (from the map) to be the same concept. I recommend a brief sentence *not* in a keyed area that says something like, "Once the zombie brigands in areas 3-5 notice intruders, they prepare to snipe from the barely-noticeable arrow slits."
Eliminate "Attacks with the sword when..." because it implies the brigand won't attack with the sword if one PC engages it in melee, but some other PC is still in the room below the arrow slit. Trust the referee to know/decide when the brigand switches to melee. Better, if the brigands have a *goal* (prevent theft of a particular thing, for example), then state that goal, so the referee has a better idea of how you intend them to prioritize their action.
Your room names could be better. A good room name gives a first-glance reminder about what's in the room, and sometimes allows you to eliminate words in the description. Offhand, instead of "Entrance," I'd use maybe something like "Warrior Reliefs" Instead of, "Gathering Hall" (what about the room makes it a gathering hall — none of the trappings support that), maybe "Sniper Gauntlet."
Please take this in the constructive spirit I intend: I get the feeling that you don't currently run a D&D game or run modules produced by others. The omissions and design choices make me think you aren't familiar with what players will be asking about the environment, and aren't familiar with players solving most tactical & strategic problems without tools being put in front of them in the applicable rooms.