I think you have to do this for yourself. But at first, you need the right tooling when you are developing.
I'd really recommend you to start with test driven development, so you have a lot of unit tests. Then write some integration tests to check if your classes / subsystems work together properly. Then build a monkeyrunner to test you UI controls. After every change to your code you should run all the tests and they should all pass before publishing.
When getting an ANR it's important to use the profiler.
As I understood from your question, you just get an Exception. I think it would be a good thing to create an unhandledExceptionHandler. In this handler you can report the error to a web service you have to write. But you have to be a little careful here. You never want to generate an exception in the unhandled exception handler (by reading from database, or doing communication).
In my opinion it is always a good thing to write an unhandled exception handler. In this way you can close your application properly, report back to the developer (you) and warn the user. In this way the user doesn't get the "com.yourcompany.yourprogram has stopped working" dialog. Getting this dialog will lose the users fate, just like you said with the user wanting his money back.
Now, if you have already deployed your application, it might be a little late to do these quality changes to your application. But keep it in mind for possible other apps.
