This is a Panda issue.
Google has said many times with affiliate sites that use the same content that if they do a better job than the original site it will rank them. So its not all bad when you look at it from that point of view.
However, Google loves unique content and will do its best to rank sites first that have the unique content. I have a business in the office space industry and a few years back we used to aggregate office apace listings which were shared amongst 30+ sites. The display of these listings would be different for many searches but the content was the same as all the other sites. This slowly put us in a PANDA DEVALUATION (there is no panda penalty).
After re-writing them with our clients we saw a significant change once the content had be re-crawled.
So it can have a great effect. If Google starts to see that large parts of your site are duplicate content it will start to question the authority you have in your industry.
Could you offer and incentive to your customers to write something unique? And also maybe inform your users not to copy and paste their own content on your site as this could affect them negatively in Google?
If you are an authority could you tell users that if you want to be listed it must be unique? Or if its a paid service have an ad on service for a few bucks where you write a professional description? Might become a nice additional income?
Just a few ideas