Apple - LSOpenURLsWithRole() failed with error -10810 Can't open 'Install OS X Yosemite.app'

That would seem to imply the executable within the package isn't actually executable.

Where did you get it from?
If not Apple, I'd leave it well alone. If it was from Apple, try this in Terminal

chmod +x /Applications/Install\ OS\ X\ Yosemite.app/Contents/MacOS/InstallAssistant

I had this error with Pentaho 8. This command solved it for me: xattr -dr com.apple.quarantine '/Applications/Pentaho/design-tools/data-integration/Data Integration.app'

OSX will "quarantine" files that are downloaded from untrusted sources.

You can see if this is your problem by listing the xattrs. cd /path/to/your/ApplicationName.app xattr -l Contents/MacOS/*

If you see "com.apple.quarantine" then that's your problem.

I mysteriously got this on Yosemite for the Calendar app. Launching the actual binary worked for me.

bash$ /Applications/Calendar.app/Contents/MacOS/Calendar &

There did not seem to be a permissions issue that could be fixed with chmod.

The symptom I got originally was "The application "Calendar.app" is not open anymore" when attempting to click calendar reservations in Mail.app.