Is there a recommended “Android way” of displaying errors to the user?
For example, suppose I catch an exception in my Application/Service and the user needs to be informed about it – is the usual approach to display a toast/pop-up dialog if the application is being displayed and a notification in the notification bar if the application is in the background?
Depends on the type of error, of course. But never show an error in the notification bar.
As a general rule, try to gracefully continue app execution, without informing the user.
If the error is such that your app cannot continue with what the user asked it to do no matter what, show a Toast.
EDIT: As mentioned in the comments in my reply, you can show an AlertDialog or a Toast depending on the severity of the error.
In my opinion, however, using a notification to show an error message is only applicable for very specific use cases as in downloaders or music players where the app is performing a user created task in the background.