I've posted a question on Stack Overflow, asking whether it is possible to ignore Exceptions that never pass through my code (i.e. non-library code). Or how to break on exceptions at the point where they pass through my code instead of where it is thrown. I'm explaining the issue in great detail on Stack Overflow:
I'm reposting this question here, because I'm particularly interested in having this functionality in IntelliJ IDEA. If that's not already possible, I'll be happy to open a feature request with all your suggestions!