I keep all my weapons on 1 chest, all my apparel in 1 dresser, and miscellaneous items in a cupboard. The apparel dresser is a mess. Why doesn't it auto group armor pieces together?

The answer is simply, you don't. As of now Skyrim does not have chest organization for some reason.

if you have a PC you can try this mod: http://skyrimnexus.com/downloads/file.php?id=1227

I find this annoying too, but then again I also find it annoying that they defaulted the same button you use to place an item into a chest as the same button to take ALL from a chest.. yeah, that doesn't cause problems.

i put all money, necklaces, jewels, etc in the safe in solitude

weapons and armor a the chest at the foot of the bed

all smithing materials in breezehome

and thats about it

I have full sets of armor for most of them and none of the sets have all 4 pieces grouped together. For some reason all of the shields are together, but nothing else.

lol, there are a few inconsistency's like that in the game. Bugs me.

Weapons in a chest, armor in a dresser, gems in the night table, smithing in a cabinet, dragon parts in Lydia's room, food in a cabinet, ingredients in the satchel, and potions in the chest, although some are in a burlap sack...and I just threw a few dwemer pieces on the floor for Lydia to play with in between eating bread.

There seems to be some sort of organization, but not really, if that makes sense. Some stuff seems to be grouped together but not others. I make it more manageable by keeping food in the kitchen area, the ingredients near my alchemy lab, the potions in another cupboard, weapons in another, etc.

mine is basically

in whiterun

top floor
---------
next to my bed 1 draw = armour,cloths,shields and helms etc
next to my bed 2 draw = all weapons
near foot of my bed = rings and neckys
near bedroom door (inside) = old keys

top floor draw 1 = junk to sell and other misc items
top floor draw 2 (near bedroom) = jewels, ores, soul gems etc.

servants room chest 1 = scrolls
servants room chest 2 = stolen stuff

ground floor
---------------
near front door = potions and booze
barrel under stairs = arrows, dwarfen stuff like cogs etc.
draw near barrel = food
in alchemy room = ingredients