I am having the same problem, also on 10.8.2.

Both 3.5 and 3.5.1 will only show Unarchiver preferences when double-clicking an archive. It will not extract the archive unless I then Open the archive.

I deleted the preferences in ~/Library/Containers. This did not help. Preference files are re-created, but archives are not extracted on launch.

Choosing File->Open does still work. I noticed that the sandboxed app told me to ask for permission to extract to my Desktop. After that, quitting The Unarchiver, and double-clicking the archive still does the same thing. It just displays Preferences.