The main problem with no traps is that the game is so buggy that less than half of you military dwarves will wear armor properly, and you will have insane micro-managing trying to even get half a dozen of them outfitted. Basically, the military side of the game is almost completely broken.
For instance, one of my dwarves, after having upgraded to chainmail, has decided his leather leggings would go better in his right hand, which is also holding a water skin and his shield, no of which will be usable like that.
Half of my other dwarves have backpacks or waterskins or socks or something in their shield hand, and there is NO way to make them drop that, making the shields useless. I wish Toady would hurry up and make a release that fixes the military at least somewhat.
EDIT: Also, can't get the dwarves to equip the Great Helms I've just made, either under chain OR plate armor.
I have only the problem that my dwarves take off their leather armor (all of it) when switching to chainmail
chain and plate are layered semi-properly; the leggings are lost when equipping plate over chain.
However, I can't recall if that's normal or not. losing the leather armor isn't normal. I'm sure my last few fortresses had their military clad in both leather and plate.. Hmm.. Maybe I skipped the chainmail those times though..
As for your problems with dwarves holding stuff in their hands, I think it has to do with the waterskins. They are not functioning / broken at the current release ( and have been for quite a while). If I recall correctly, there's a problem with filling up waterskins that results in them not being dropped / equipped properly. Do not set your military to use waterskins, only food rations.
Edit: What sane dwarf would drink water anyways?
Edit2: I do not know if, for your current situation, setting your military to no longer use waterskins makes them drop them and fix your problem.. If not:
1) forbid all waterskins you want dropped
2) save, exit, and open body_default.txt in raw/objects folder
3) remove [thOUGHT] (fully capitalized ofcourse, sorry, forum scripting can't take that) from [BODY:BRAIN]
4) restart DF, load game
5) all your dwarves, and other beings with brains will have passed out due to lack of thoughts, dropping all their stuff in the progress
6) save, exit
7) put back [thOUGHT] in [BODY:BRAIN]
8] restart, load and behold! Your dwarves won't pick up those waterskins again
EDIT3: as for great helms, I think those are simply too big for dwarves (it's the only helmet with [MATERIAL_SIZE:3] in the raws, the others have size 2)
