I believe the root cause of the problem is that the config file "SQLDeveloper.app/Contents/Resources/sqldeveloper/sqldeveloper/bin/sqldeveloper-Darwin.conf" sets the default java home to
and this location does not exist on Mountain Lion unless Apple's Java 6 has been installed.
The solution described above to put the path to an existing java home directory in $HOME/.sqldeveloper/jdk seems to be the best way to fix this issue, e.g. by doing
/usr/libexec/java_home > ~/.sqldeveloper/jdk
What SqlDeveloper should do is of course to change "sqldeveloper-Darwin.conf" to do