Feedback to the user when a background task fails

[monsieurtanuki]

Problem

Sometimes, background tasks fail.
Like in the real world, uploads and downloads sometimes fail.
The problem is that we don't warn the user. And we just retry the task, again and again.
In some cases, retrying is the correct approach: if the connection was down, if the server was down.
But there are cases where the server does not accept our data, and never will. For instance, if the image is too small (cf. #4488).
And in that particular case, we just get a confuse status ('status not ok') and a localized message (e.g. 'Das Foto ist zu klein. Bitte beachten Sie, dass Sie kein Foto aus dem Internet, sondern nur Ihre eigenen Fotos hochladen dürfen.').

Proposed solution

Let's say that there are 3 possible cases:

1. the background task works OK - no problem
2. the background task throws an exception - typically connection / server down - we'll retry
3. the server returns status not ok - this is problematic

In case (3), we have good reasons to say that the background task will always fail, and it's no use running it again.
But how do we warn the user that the background task is in error and the local data is to be discarded?
A system notification? A dialog that gets opened from most pages if something like that happens?