I've joined the Mac Developer Program and was able to sign Dia.app for
Mac OS X.
Depending on your security settings Mountain Lion's Gatekeeper might
check this signature
and cause problems.
Thanks to all donors that made this possible!
As Mountain Lion also removed X11 from the detailed installation, I
added an X11 check to the app
that will tell you about the problem and automatically take you to the
XQuartz website,
allowing you to download and install XQuartz.