I've recieved and sent video messages with no problem in beta, but I had just recieved a message and the player loads and everythings ready to go, then it doesn't load the actuall video.
For me I was able to resolve that at a friend's place by updating their Internet Explorer and their Adobe Flash for firefox.
I got that idea from this post, it has other steps to try as well should the above not help;
Hope this helps you ! :-D