I encounter this on my site all the time. Because of the limitations of the platform we are using we had to create a lot of duplicate pages in order to have the same subcategory in different category options.
The effect this has on SEO is a bit tricky. In my opinion it is very harmful because I am diluting the value of the traffic that comes to the site. I am taking 100% of traffic and exponentially decreasing it as different people go down different paths. Aside from that, the more clicks it takes someone to get to a particular product, the better chance you have of losing that customer. Every click is an opportunity for them to leave your site.
I have been fixing this problem on my site by redirecting duplicate pages and eliminating the multiple paths. Since doing that, my page values have increased and I am seeing less of a bounce rate. A slightly higher conversion rate as well. It sounds like you have one product that falls into multiple categories. If that works for you as far as how easy it is to find that particular product, I wouldn't change anything. If you want to see an increase in PR, conversions and traffic I would recommend eliminating some of the pages.