Checked exceptions are great in some cases. They are huge annoyance in others. The complaint is that the language does not provide tools to separate these cases

Checked exceptions are great in some cases. They are huge annoyance in others. The complaint is that the language does not provide tools to separate these cases - you can't just say "this method doesn't handle exceptions, pass it up" or "ok, now I want all exceptions to be handled, so tell me if I forgot something". It does not give the programmer control. Java has excellent facilities to make it happen - annotation, static analysis tools, extensive array of code checkers - but all this has to bow to the built-in mechanism which is crude and inflexible.