aLogcat

An app equivalent of logcat from the terminal. You can filter by importance in the settings: see only errors or view general debugging info. The result can then be filtered by keyword so if an app has problems you can send just the relevant logs to the developer. But watch out, the filter remains in place unless you remove it!

It might not work on Android 4.1+, since apps are not allowed to access each other's logs. In custom ROMs with root access it should still probably work