Geneious versions 5.6.4 and earlier are not digitally signed, and you may run into issues with the OS describing the application bundle as damaged. This is a warning generated by Mountain Lion security settings being set to allow only apps from the Mac App Store and identified developers. To fix this problem, go into:
Preferences→Security & Privacy→General and switch 'Allow applications downloaded from:' to 'Anywhere'.
You should then be able to proceed with the installation. Geneious versions 5.6.5 onwards are digitally signed so will install under Mountain Lion with the default security settings.