In my organization we almost never finish all the stories in the Sprint, and most of the stories are finished about 80%.
One reason for this, is that many times testers don't have enough time to test all the stories, and developers don't want to test. Another reason is that the teams are usually too optimistic so they commit to more than they can complete, and no one really cares about that, so they continue to do it each Sprint. Usually testing, bug fixes and last polishes remain on the task board after the Sprint is over.
The R&D manager believes that its not that bad to leave some bugs unfixed or to skip some non critical implementation, because then he can have usability test for the new features faster. Nevertheless I think he would be happy if the team could finish all the testing and bug fixes, but if not that's completely okay for him as well, because there are always some stabilization (hardening) sprints at the end in which the smaller stuff will be taken care of.
I'd like to ask you, what do you think about this development method (which is not pure Scrum, but a more flexible/weak version of it).