I had this problem on 3 of my computers and thought it was a Mac issue. Well maybe it is but I have been reading online that PCs are having the problem as well. Now I am not 100% sure what is causing the issue, whether its a setting on the computer, browsers, or in facebook itself, or even in a plug in. But I do know a solution:)
In your address bar you will see something like: http://www.facebook.com or www.facebook.com
The problem is that your browser is looking for a secure connection to view the video. So to view it you need to make sure there is an (s) in that web address like so:
Do you see the (s)? Type that in and reload your page. The video should now play. And yea you will need to do this each time you want to view one but at least its working.