With the recent of banning by Facebook auto-bots, it is to your benefit to ensure that your Facebook App does not violate any of the Facebook policies. It’s also important to make sure that users do not consider your App as ‘spammy.’ If your application publishes on users’ wall, feed, or photo albums, then it’s worth checking the users’ feedback from time to time.
To help developers, Facebook has recently added some statistic and metrics within the Insight tools. It is called the Negative Feedback metric. This new metric is available from within Your Facebook App Developer page, such as shown below. You can see what are considered Negative Feedbacks: Story Hides, Spam Reports, and Spam Reports by Posting User. On the other hands, Positive Feedbacks include Story Likes, Story Comments and Story Clicks. Naturally, you want to minimize the Negative Feedback and maximize Positive ones.
There are several ways to go to the Negative Feedbacks metris. One of them is to go to https://www.facebook.com/insights/. This will lists all of the Apps that you manage or develop. Then select View Insight link within the App that you want to check. Once you are in the Insight page, select the Publish Category link on the left sidebar (see picture above).
Another way is to enter https://www.facebook.com/insights/?sk=ao_yourAppId (replace yourAppId with the numeric id of your app).
Another way is to go the the developer page: https://developers.facebook.com/apps and select the See All link on the Insight section (circled below).
Unfortunately, I know of no official metrics that states what Negative Feedback will trigger an actual ban of an app, but to better understand this subjects, here are some recommended readings: https://developers.facebook.com/blog/post/521/ and https://developers.facebook.com/docs/guides/policy/examples_and_explanations/user_feedback/. Be aware that the Negative Feedback should not be considered the only reason that an App may get banned. For example, see here: http://venturebeat.com/2010/10/17/wsj-reports-facebook-apps-including-banned-lolapps-games-transmitted-private-user-data/.