How can I force the Market to reinstall an installed app? I have an app, installed from the Market, which I just updated. The "updating" notification was present for several hours, so it appears to have gotten stuck somehow.

I believe it now claims to be the current version, but to be sure, is it possible to tell the Market to re-download and reinstall the current version of the app?
As far as I know there's no way to tell the Market to reinstall an app.  I was hoping you could do it through the Market website but I just tried and it refused to install an already-installed app.  (Which bothers me because my phone and the website will definitely be out of sync regularly, I do too many third-party restores and so on.)

That said, you could clear the data for the Market (Settings -> Applications -> Manage Applications -> All -> Market -> Force Close, Clear Data) and reboot your phone, then start up the Market again and look to see whether the update is available again or not.  If it's not then you can trust that the latest version is installed since it grabbed that info directly from the system, and if not you can attempt the update again.