OK, so I'm designing a 'monster of the week' game where the players are tasked with hunting down a single monster and stopping it before it kills again. The default setting will be "Swords and Noire".
The game will be diceless and feature a grid-based combat system resembling 'Battleship' and 'Clue'. Conflict is resolved through deduction or guesswork.

Monsters and players will have hit locations represented with 'Physical Grids'. For human characters this will be a 3x3 grid looking something like this:
[table]
[tr]
[td]Left Shoulder,[/td]
[td]Head,[/td]
[td]Right Shoulder,[/td]
[/tr]
[tr]
[td]Left Hand,[/td]
[td]Torso,[/td]
[td]Right Hand,[/td]
[/tr]
[tr]
[td]Left Leg,[/td]
[td]Groin,[/td]
[td]Right Leg,[/td]
[/tr]
[/table]

Monsters will have many more rows and columns in their grids to represent all their different wings and claws and tentacles and whatnot. Generally though these will be organized from "Left" to "Right" and "Top" to "Bottom".

Furthermore, player characters will also have Social Grids on their character sheets. Players will come up with NPCs that are associated with their characters, and rank them on their Social grids from "Friendly" to "Hostile" on the horizontal axis, and "Well Known" to  "Met Recently" on the verticle axis.
These NPCs will be prime targets for the monster to kill if the players don't hurry up and stop it first.

What I need now is a Mental grid for the investigative elements of the game.
Players have to stop the monster from killing off characters on their Social grids. To do that, players will have to fight the monster. To fight the monster, the players will have to find the monster and figure out its weakness.
This grid will entail knowledge, skills, language, perception, sanity, and (optionally) magic.
The squares within can be treated as hit locations if the monster has certain abilities of it it hits a human in the head.
I'm just having a little bit of trouble figuring out what the dimensions of the grid ought to represent.
Do you guys have any suggestions?

I'm big on symbolism, even if it turns out to be mostly flavor. For your idea here, I would probably choose a grid layout that was say the 5 classic elements of eatern and western thought, or one of the tarot spreads like the Mirror Spread. You could do axis about strengths and causes and so on and use a clue like reduction mechanism where you fainlly fill in the "heart" which is the vulnerability, the key npc, or the last clue needed.

....If you think the Monster's Physical Grid is complex, ........ it is still nothing compared to if you intend to cram "knowledge, skills, language, perception, sanity, and (optionally) magic" into an Investigation Grid.....
But that is just obvious.
It may be in order to meke it simpler.
Physical Proof - Gut Feel/Sixth Sense, or even Physical Proof - Gut Feel - Sixth Sense/ESP
on Horizontal.
But what on Verticle?

Knowledge-
Deduction-
Legwork

Might that work?

                        Catelf.

Catelf: I like that.
I think I might change the names around a little bit..

Here's how I imagine this thing working now:

When you create your character, you can put a weakness into a square on your grid in order to put a strength in another one. You can keep doing this until each square is filled, but you can only put one strength or weakness into each square.

Strengths allow you to find clues to use in locating and defeating the monster*.
Weaknesses give the monster openings to attack you.

*Locating the monster may mean finding the monster's lair, or finding out where the monster will strike next, or, if the monster has a human form, finding out who the monster is.

Rows and columns may determine where and how you find clues, and what sorts of clues you can find.

Generally you will find clues by going to scenes where the monster has struck. Some characters will collect clues and take them back to the lab for analysis. Some characters can pick up scents and maybe relate them to that of creatures they encountered in the mountains of Cimmeria or whatever. Some characters might scan the area and have flashing prescient visions.

That's the general idea so far, though I am a little lacking on specifics at the moment.
Thanks guys!