The conclusion we came to was the same as this article and we calculated it using almost the same route. For cnn if 1,000 people like a story, given that there are 400,000,000 Facebook users and if we assume my friends visit cnn with equal probability as other Facebook users and that I have 300 friends, we get that their is a ~1/1000 probability that my friends like a cnn story. Sum up over 10 major stories that day, we get that I only have a 1/100 chance of seeing any activity at cnn.com from my friends. And this is the case for cnn, one of the largest websites in the country; the probability of seeing any friend activity on a smaller site will be much much lower. The numbers just don't work out for mainstream adoption of the Facebook like button.
This does however work better on a site like yelp or pandora, where if my friend ever liked a restaurant it will stay relevant for a longer period of time. Still, I think that the Facebook like button will only make sense for a few websites on the entire web (and likely not one that anyone who is reading this is working on).