Just got the notice through Hazel that v2.3.9 was available, so I used the in-panel update, it downloaded, I clicked "Install & Update", authenticated successfully as admin (I'm running as a full admin account)....but then Hazel said it didn't have permissions and mentioned that I might be working off a disk image (I'm not). So the automatic updater didn't work properly for some reason this time....once I authenticate, it should have all the permissions that it needs.
So I downloaded the latest Hazel from the website, launched the Prefpane from the disk image, it offered to replace the current prefpane and I authenticated and it ostensibly did the update and loaded the Hazel prefpane view in System Prefs...but it still read v2.3.8. I then quit System Prefs and relaunched it, noticing now that Hazel's About tab read 2.3.9...yay! But it also said that Hazel was Stopped. Clicking on the "Start Hazel" button did nothing. The menubar item showed that Hazel was running, so I stopped it there, then tried to use the System Prefs "Start Hazel" button again....nothing.
At that point I just decided to reboot and after everything came up, all was well.
Not sure if I'm a lone issue or something, but it seems like the Hazel updating process needs to get a little more complex, perhaps shutting down the old Hazel and starting the new one, or Hazel needs to check to see if there's a newer version of itself and shut itself down properly to let the new version in. This kind of thing shouldn't require a reboot....