Same error on linux mint 15 32bits java 7.
I hope this will fix soon...
Try to start using "sudo sqldeveloper"
As I remember it was a variable which Gnome 3 set on start and value in this variable leads to sqldeveloper crash.
Thx that's works but I saw on a other topic a better solution.
unset -v GNOME_DESKTOP_SESSION_ID
cd "`dirname $0`"/sqldeveloper/bin && bash sqldeveloper $*
You're right. Used the same solution before but couldn't remember the name of the variable. I just switched to Mate then to XFCE and happy now without variables, sudo, etc.