The current Curio seems to run just fine on Mountain Lion (Mac OS X 10.8) although there are no special Mountain Lion features enabled, of course.
We thought there was going to be an issue regarding iCal syncing since, in 10.8, Apple separated iCal into Calendar for events and Reminders for tasks. However, since we're using their CalendarStore API it seems to work very well between the separate apps.
Update: One thing I should clarify is that Curio 7 and earlier releases are not signed with one of the new Developer ID's from Apple. This means, if this is the first time you've run Curio on this machine, Mountain Lion's Gatekeeper won't know if it's a trusted app and will report that it can't be launched. Fortunately, rather than disabling Gatekeeper in System Preferences there's an easy workaround: just right-click (or Control-click) on the app in the Finder and choose Open. Once you've okay'ed the open Mountain Lion will remember that the app is safe. More info about Gatekeeper can be found in Siracusa's awesome Mountain Lion review.
Update 2: Apparently there is an issue with Curio 7 pens and brushes sketching mode. We are investigating.
Update 3: Quick tweak made and Curio 7.4.4 has been released.