Yes, 1.6.0_29 is the latest Java version available from Apple.
Does deleting the yEd profile directory: /Users/stephan/Library/yWorks/yEd help with the issue? (If you have custom palette section, keep a backup of this directory.)
If your Java installation is OK, then there might be a problem with one of the files from your yEd profile.
yEd 3.8 runs here on Mac OS X 10.6.8 with Java 1.6.0_29 (64bit Core 2 Duo Intel).