A Google Places Help thread has one business owner frustrated his business listing is 93% complete according to Google Places. He has tried everything over the course of a few years to complete his profile, but nothing he does works.
He is at the point of wanting to delete his business listing and start "fresh." He asked, "What are the implications of deleting listing and starting fresh?"
Ryan Meley responded in the thread, and his response was noted as the "best answer" by Googler, Cecelia. Ryan said:
The reason I would not recommend starting over is if you have any decent positions in search results, this is most likely thanks to sources outside of your listing. By deleting the listing, these will disappear. Granted, they should come back over time, but in the meantime you would not have a local listing. This process can take some time... many weeks in most cases. In addition, if the review is posted on a third party website, it will come back evenentually no matter what. Finally, it is my personal thought (unconfirmed) that time is a factor Google applies (to a small degree) in the display of local listings i.e., the longer you're up the better you will do... all other things equal.
As you can see, there can be serious repercussions when you remove a listing. Your rankings can drop and thus lose some business.
Forum discussion at Google Places Help.