It's hard to summarize the problem in a title, but I was able to extract a reproducible test case.
Consider the attached project (create a new workspace, "Import Existing Project Into Workspace", from the attached archive).
TestGroovyNull.zip
Look at the Java class named JavaExt1.
In the Project Explorer all classes seem to compile fine. But if you open the editor on JavaExt1 you'll see this error on line 10:
The method getFoo() is undefined for the type GroovyExt2
If you then go to TestGroovyNull project settings and uncheck Java Compiler | Errors/Warnings | Enable annotation-based null analysis, the above error goes away.
It's not clear to me whether the code is actually compiled or not, and hence it could be run.
Please note that the error also goes away if you keep annotation-based null analysis enabled but remove method test.GroovyExt2.foobar()... really obscure to me why.
This is a bit annoying because it's forcing me to disable annotation-based null analysis on a real project for now.