CS4 is not compatible with the current 10.8.x versions of OSX.
Do you mean the installer isn't compatible? I'm running CS4 on my older iMac with 10.8.3 OSX with no problem.
I'm not running the whole CS4 suite on my Mac under Mountain Lion but I am using Dreamweaver CS4 with no problems.
Have you got Adobe Air installed? If so uninstal it and also run the uninstaller for CS4 and then try again.
I uninstalled every Adobe product I had, including Adobe Air, and removed all Adobe items from Preferences, System, etc. After creating a new User with admin privileges I rebooted in Safe mode and still have the same problem. I have worked through all ten of the solutions Adobe mentions on its Web site--all with no success.
This is all terribly frustrating. I don't really have $500 to upgrade to CS6 and need this software badly for image processing and Web management.