Sometimes if you get the "inventory is full" message you will suddenly find that you cannot use Nano/Treatment kits, open chests, loot bodies, or any other effect that takes a single right click to activate. This has happened to me several times now, each time while in a mission, the last time it happened I kept trying to over-fill my inventory just to get the message and see if the bug would happen. It took a few times but eventually it did happen, so that means it must be reproduceable I'd figure. The only two ways I've found to un-bug yourself when this happens is to either log, or find a way to get the overflow window to open up, e.g. completing a mission and get a reward and token.