I have a trade with a couple hundred items, but when I save it I get the error in the title.
I had tried removing and readding all items, but the error remains. I do not know which items cause this, so some sort of indication would be nice. Or offering me to remove the items from a pool. Or maybe just updating the backend representation of my bot's inventory might do the trick?

From what I have quickly checked, there are 2 bushwacka and 1 loch'n'load duplicates in your inventory. Are you trying to add them to the trade? I can see why it does not save.

About the bug itself, as it is a script bug rather than a database bug, we cannot fix it right away as it is more complicated than it looks. So do not add the bushwacka and loch'n'load to the trade for now.

I just tried withdrawing all Loch-n-Loads and Bushwackas via trade offer without putting anything from me intto the trade offer, but "the system cannot identify the items in [my] deposit" http://i.imgur.com/rnoyTyh.png
So how do I fix this?

I tried doing that with the remaining items of the type you mentioned and the transfer just remains "queued"
That is also blocking another withdrawal.

I've tried resaving the trade without the LoLs and BWs, but it just remains "saving" indefinitely.