When I tried to embed my video "how typical Facebook spam works" on my Facebook wall. I could not see the thumbnail of the video. All I could see was the link to my YouTube video. This was really something I did not want to do. I wanted people to see video on Facebook. I really don't know if the issue is/was on YouTube site or Facebook site but I could find a solution to this problem.
You can do two things. Either use some other browser. I was using Google Chrome. I could not see the thumbnail with Google Chrome. So I tried with Firefox and I was done. Later again when I tried with chrome I faced the same issue. So I cleared the browsing data, cache ,cookies etc. I tried again and bingo! It worked!
So either use some other browser or clear the browsing data. I think latter one is better. Please post your opinions in comment area. I will be posting the screencast of this soon!