How weird. Having tried several times to delete one folder on the drive (to be told it was unreadable), I checked the folder properties as per Greenbank above, then did a virus scan on it just for the hell of it (negative), and then tried to delete it... and it worked!
Er, thanks Greenbank.
I see that when you use the "eject hardware" tool, the drive shows up as having two components, Cruzer Micro and a generic volume with appropriate drive letter. The Cruzer Micro does not show up in Explorer.