A thought. Can a mind controlled character be made to unequip itself from an item it may be carrying or have as your free action?

Only if you have a legal action to give it that would cause the equipped item to be KO'd or otherwise removed. As of now, I am not aware of any way to do this. There is no way to just voluntarily un-equip an item.

you could have it equip another item, which would KO/unequip the original item.

which would require you to have the foresight to have brought an item to "give" to your opponent, as when you return control of the character to your opponent, the new item would remain equipped to it.

It's possible, but are you feeling ... generous?

No, none of that is possible. Even if you had your own equipment, a MC'd character can't equip it.

E&C, under Equip:
Like I said, as far as I'm aware, there's no way to do this currently.

well, there goes that broken idea ...