Before installing on Mac OS X 10.8 Mountain Lion, you need to change your machine's default security settings. This is because MultiBit Classic DMG files are not currently signed with an Apple Developer key. Earlier Mac OS X operating systems are not affected.
The setting to change is in the 'Apple menu > "System Preferences..." > "Personal" section > "Security Privacy" > "General" pane'. The setting to set is the 'Allow applications downloaded from: Anywhere'.
Without this setup, when you try to open the DMG file you get an error:
"MultiBit Classic” is damaged and can’t be opened. You should eject the disk image.
In due course we will start signing the MultiBit Classic DMG files and this problem will disappear.