We have a written checkstyle extension that run on our test server. In your sample it would test if HorribleException was documented.
The ArrayIndexOutOfBoundsException will detect with a code review. In your sample code our goals required to throw a InvalidArgumentException instead a ArrayIndexOutOfBoundsException. The documentation of it will be find from test server.
The ArrayIndexOutOfBoundsException can be a warning in FindBugs. But I am not sure.