I'll avoid quoting a whole bunch of stuff and get straight to the point:
I agree with all the points Bastien raised.
Furthermore, I think it would be best if the problem will be reported *automatically*.
You can allow the user to comment on the problem if they have anything to add directly from the notification ("The problem has been reported. [comment]"). The "comment" button would open a simple screen in which they'll be able to comment, but there shouldn't be a "progress" screen for comment submission - it should be done in the background. There's no real reason to make the user watch a progress screen when they report a comment, and no real reason for them to close the dialog manually.
Another thing worth considering is having a button in the notification to re-launch the program that crashed if it was a desktop app and not a background service.
Users should be able to disable this kind of automatic reporting in the privacy panel in Settings.
Ideally you want the reporting process to be un-intrusive and to take little to no time from the user.
If you make the user wait more than a minute just to report an issue, they'll not do it again ever.