It happens randomly to me(usually when switching weapons after removing a favorite)...but sometimes I can have my left hand with nothing in it, and a sword in my right hand. As soon as I use a spell from my hotkeys, my left hand always has a spell on it now.

How do I free up my left hand(or right) so I can use a single handed sword only with no shield?

Go in to magic sectio on the menu and unequip.

Right, but there have been occasions where it happened without me doing that. I guess I'm looking for a hotkey to do it...or an explanation of why it happens by itself sometimes.

If you equip a weapon then unequip it, it will leave you with your bare fist. This may be what you did.

I just added my shield to the favorites list and assigned it a hotkey number. What I've been unable to figure out is how to assign a spell to my right hand and cast while I'm still holding my bow in the left.
It seems no matter what I do, casting gets rid of your weapon.

A bow is a 2-Handed weapon, you can't use anything else while you have it out...

Yea but it happened with the left fist, the hand that didn't have the 1-handed sword equiped. I am moving from Mage to 1-Hander since my Destruction and Conj are maxed now. You can use a 1-handed sword to block with as long as the other hand is not in use(spell attached to it).

Oh well, I guess I can just hit Q and unequip the spell quick enough but was hoping to simply hit the Hotkey button again, which we all know makes the spell a duel wield. I suppose that is the reason you cannot unequip a spell...maybe they should program it so that if you HOLD the hotkey for a second it unequips, double click to duel wield. That would be ideal.

I'm 99% sure it's an interface bug/oversight.

The issue is with upgraded/enchanted weapons. If I use two regular swords (Steel, Daedric, wehatever) and assign them to a hot key, when I switch from Sword/Sword to Sword/Spell I can just hit the hotkey and go right back to Sword/Sword. However, if either of the weapons are upgraded/enchanted, it will go to Spell/Unarmed, then unarmed/unarmed with the press of the sword hotkey.

It's really, really, really annoying. I have to open up my menu to re-equip my off hand weapon every time (which isn't fun when playing a dual wielding/illusion/restro assassin).

think i've got the same problem, what heppens with me is that, say i'm dual wielding spells (it's 4 on my hotkeys), then a switch to a bow (1), then a bit later I switch to a one handed sword (2), my empty hand will have one of the spells I had (sometimes hours) earlier equipped, forcing me to manually open the menu and unequip it.