I am currently running the Studio Edition Version 184.108.40.206.0
Google gave me a good first place to start : A Mountain Lion Ate My JDeveloper. While this sounds like the right solution, I am going with a simple hack for now; it is to use JDK 1.7 and ignore the warning seen at startup.
SetJavaHome /Library/Java/JavaVirtualMachines/1.7.0.jdk/Contents/HomeSo far, so good and I am able to see my current projects and compile my code.
You mileage may varies.