I bought Aperture when running OS X Lion and ever since I upgraded to Mountain Lion, I've always received this error when trying to launch the app. The error in its entirity is:
Aperture cannot be opened because of a problem.
Check with the developer to make sure Aperture works with this version of OS X. You may need to reinstall the application. Be sure to install available updates for the application and OS X.
This report will be sent to Apple automatically.
Does anyone have any ideas as to how I can resolve this issue?
No, uninstalling Final Cut will not restore the missing framework. Only reinstalling Mac OS X will do that, if you do not have a backup. But Final Cut will be continuing to work, after you reinstall Mt. Lion.
You will be able to use Aperture and Final Cut hand-in-hand. It is just a question, what you install first.
This problem has been around for a long time, see: Aperture 3.x: Aperture unexpectedly quits if Final Cut Express 4 is installed