We've all been there - the Sprint is over, the team have been working solidly for two weeks and yet half of the items it contains are still work in progress.
While it's not the end of the world for any given item one of the benefits of breaking work into sprints is to define and deliver work in predictable increments. That doesn't work if the promises made during planning (at the start of the sprint) are not being delivered in the sprint review (at the end of the sprint).
If stuff the team accepted at planning is consistently carried over then either:
The team is over-committing during planning - either in the amount of work they take on, or accepting work which isn't properly defined OR
They are getting distracted by things getting added to the sprint after planning which were not part of their original original commitment.
In particular, by just moving things from last sprint to next you are kind of assuming that everything slipping out is more important than everything new that needs doing - which is rarely true.
As a product owner, the team's ability to plan accurately is crucial for managing stakeholder expectations, so if this is a problem when I take over a team then getting it fixed is my top priority.
Some ways to make this happen:
Make sure every item I need is properly refined before Planning
Ask for an hour between Sprint Review and Planning (e.g., over lunch) to make sure the slipped items are correctly prioritized
Push back hard on any "urgent" issues added mid sprint; I don't always win, but I always try :)
Of course, the Product Owner is not enough - so this is also a great retro topic for the whole team