Since there are a few different opinions on this topic, I figured I would weigh in.

A bad backlink profile can effect a sites SERPS, but it depends on the site. If your site has a mostly White Hat, clean on-page strategy, and mostly good backlink history, you should be fine. If your site has a lot of authority, then the bad back links definitely won't hurt you, they might even help you (read this), but be careful, because you still don't want to get to careless.

I would say that you should remove as many links as you can, and then forget about the rest. If you move forward and build a strong link profile that is filled with editorial links, and legitimately acquired reviews, you'll be fine.

Best of luck

-Bryant Jaquez