From what I've seen, the biggest way people use it wrong is by just taking the top 5 or 10 results on the first page and plugging those into POP. Instead, because POP is strictly an on-page tool, you have to pick the competitors who are ranking partially or mostly because of their on-page strength. So I use this in conjunction with serpworx to really get the full effect.
What I'll do is disregard the huge sites; yelp, amazon, thumbtack, houzz, etc. Then I'll throw out any site that looks to be ranking based on off-page signals, like a huge amount of backlinks or social shares. What's left should be pages that are ranking based on strong on-page signals. I'll plug those into POP and compare my site against those.
Once you get the report, you have to know how to massage it a bit. When comparing for average wordcount, I don't try to hit it exactly. I'll usually try to get within +/- 25%, and I would never go above wordcount + 50%. I usually disregard a lot of the suggestions from "page structure" suggestions, especially if I feel it would break up the flow of the page (such as ol and ul, iframes, and video) and optimize around the "recommendations" and "alternative recommendations" tabs.