Tried on the commandline (both times using Grails 1.3.7) and got pretty much the same result.
That is: when I do the upgrade first things looks fine, but that is only because Grails has not yet attempted to compile the sample app.
If I try to compile it with "grails compile" or (more indirectly) with "grails run-app". I get compilation errors similar to the ones I get reported in the error message by STS.
It would seem that the sample project is either broken or not compatible with Grails 1.3.7.