Minecraft – Mobs spawning everywhere except the mob farm. What can cause this

Technically, placing torches will decrease your overall mob spawns; the game does pick a single random point within the eligible chunks to spawn a monster, and if that point is not suitable, the monster doesn't spawn. Therefore filling other caves with torches will reduce the number of spawn-friendly points, reducing your overall monster count. This does technically help your mob grinder because you don't have mobs lurking in neighboring caves counting against the mob cap (and ultimately taking it all up, preventing anything from spawning in your grinder).

The best solution would probably be to use a vast water network to drag all the mobs from all nearby caves into your grinder, so you maximize spawn area, but bring any mobs from all the viable spawn points into a single area.

Not counting mods, the best way I know of is to make sure the area you're "protecting" has a floor made of blocks which don't allow mob spawning.

Any transparent block will do the trick, such as glass or snow, and in your case maybe Slabs will be most suitable.

For more in-depth information about spawning and spawn conditions, check the wiki: http://www.minecraftwiki.net/wiki/Spawn#Mob_Spawning