Have you recently installed any registry cleaning programs? (e.g. registry mechanic).
These (however highly rated) will no doubt cause issues with Windows 7 at the moment. You could try looking at your task manager to see what programs/processes you have running that could adversly affect explorer (a screenshot would be handy too). Just type 'task manager' in the start menu search panel if right-click not working.
Until this issue is fixed you can still access the properties from the 'Organise' menu in explorer. This will allow you to continue changing 'Compatability' properties for apps.