Wikipedia is a very transparent source. This quality gives you some amazing tools for evaluating it as a source. These badges do not do the evaluation for you, though. Just because someone thinks a policy was violated, does not mean it was. You must use the information available to critically evaluate the conversation and determine its relevance to your project.
When you see these badges, check the Discussion tabs for more information about the controversy. You should also take a look at the Wikipedia policy being discussed, so you can follow and evaluate the discussion.
In this case, you would find that here: http://en.wikipedia.org/wiki/Wikipedia:Citing_sources
The neutrality badge is another very common badge that is important to understand as you evaluate the information in the main article. It is referring to Wikipedia's Neutral Point of View policy. Take a look at the page describing this policy. There will be a quiz question about Wikipedia's "core content" policies.
http://en.wikipedia.org/wiki/Wikipedia:Neutral_point_of_view (opens in a new window)