Hi Francisco,
Ok first, you should send an email to help at seomoz.org about the reauthorization problem. That shouldn't be happening and the Help team can help you out with that.
As for how the social numbers are calculated, here is a response from the engineering team:
"For the social metrics in OSE, first - they're not part of our Linkscape index. We compile those metrics from different APIs. The Twitter metrics are coming from Tweetmeme and they are page specific - not domain specific. So it's not how many people have tweeted his domain - it's how many times someone has tweeted that exact URL.
Facebook is a bit more confusing. The metric in OSE breaks out FB Likes and FB shares - however, on Facebook, when you see the number of Likes, that is a metric that combines shares, likes, and comments. It is confusing when we use Likes, because in OSE we are strictly counting Likes (like someone_liked_ it) which is not the same definition of Like on actual Facebook."It sounds like we're looking into fixing the way FB numbers work though, but it's a lower priority.I hope this helps!Jen
Please let me know if you have any additional questions.