I've downloaded Arduino 1.0.5 (for Mac) and installed it on three machines:
OS X Snow Leopard 10.6.8
OS X Mountain Lion 10.8.3 (which had Arduino 1.0.4 already installed)
OS X Mountain Lion 10.8.3 (a freshly installed machine which, obviously, that never had Arduino installed before)
On both Mountain Lion machines, the application bundle can't be run. The OS complains that the app is damaged and can't be opened. At first I thought gatekeeper might be confused somehow and disabled it, then ran Arduino, then enabled it again. This fixes the problem.
However, this is also necessary for the freshly installed machine, which makes me think that something's wrong in the Arduino app bundle and isn't necessarily a bug in gatekeeper.
This is related to Gatekeeper and not specific to the Arduino IDE. Any non-signed application will throw this exception when you "upgrade" to a new executable. (I'm seeing this happen with a number of open source applications). Which is why the re-released properly signed packages work.
You can get around it by turning off Gatekeeper, launching the affected application, and then returning your Gatekeeper settings.