I am thinking of setting up a global, default Exception handler for my (Android) Mobile application(which uses Java syntax) using Thread.setDefaultUncaughtExceptionHandler
The name is a bit misleading, because using that method will set a default exception handler for all threads.
Make sure no exceptions can be thrown from your exception handler.
If you're doing GUI stuff from your exception handler, make sure you're doing it from the right thread.
An uncaught exception will only stop the thread where the exception took place, if that also causes the process to terminate depends on any other threads that might be running.