I had the errors about "could not find the main class com.springsource.sts.grails.core.model..." and moving STS to a place with no spaces in the path fixed it. Thanks for the tip.
Please can you update http://www.grails.org/STS+Integration (unless this fact is already documented somewhere?). Otherwise how is anyone supposed to know? Paths with spaces are not exactly a new OS feature so I just assumed it would work without thinking about it.