A 12x12 chunk area at spawn always stays loaded in single player, there are numerous player designed iron farms, mob farms, chicken farms, etc. that take advantage of this fact. It is a fairly well known function of the game and is seen as a feature and not as a bug. Numerous Youtube videos exist explaining how to determine the exact area included in your "spawn chunks" and how best to use them.
As far as the reporter of this issues concerns about animals (passive mobs) there eliminating spawning elsewhere in his world they are invalid. Passive mobs have a spawn cap of 11, once every 20 seconds the game checks in a 17x17 chunk area with the player at the center to count the number of passive mobs.
If there are less than 11 passive mobs within that range then more can spawn, no closer than 24 blocks from the player and no further away than 128 blocks. They can only spawn on grass lit to light level 11 or higher (even mooshrooms, which is a bug btw, they should be able to spawn on mycelium).
The point being that animals within the "spawn chunks" have absolutely no effect on spawning elsewhere in the world. The spawn cap is not for the world itself, it is only for the 17x17 chunk area currently surrounding the player.
I will confirm Mob testing with the player and advise him to create a separate issue if in fact Mobs do not trigger a signal from his stone pressure plates as he has stated. Thank you for the confirmation photos relating to this issue Neil Lake.
I came here looking to see if this was a known issue after a player reported this problem in a thread at the Minecraft Forums. Player reports the same issue, that stone pressure plates no longer work but that wooden ones do. Player also reports that Mobs DO NOT trigger pressure plates either after testing with two (unspecified) types.
Still a concern in 1.5.2. Mooshrooms only spawn on grass, it is a bug in that mooshrooms are only ever created during initial chunk generation. If you kill all the mooshrooms in a mushroom biome then no more will ever spawn.
To solve this you have to use a silk touch pick to get grass blocks from outside the mushroom biome or build a dirt bridge to it so that grass will spread. You must then remove mycelium and replace it with grass blocks to create a "spawning pad" where mooshrooms can spawn.
Mooshrooms should be able to spawn on mycelium, but they do not.