SO, stuff gets strung out all over your characters and as they level stuff gets transferred around. I am sure we all have done the log-and-hunt drill trying to find an item on one of your toons. My suggestion is that an app is added to the character selection screen at least to check inventory of the toon you are logging into, before you actually log in. Better if you could check what was in their bank account too. Even better if you could do this from in game for another of your toons. Not necessarily having access to the item, just being able to find it.
A better improvement would be to enable a search function across all toons inventory and/or bank.