I too have the same problem, the cover has come off. Like other people on this forum I have contacted Samsung and they have told me I will need to pay for the repair. I have emailed them back pointing out given that numerous users are having this problem surely it is a manufacturing fault or not made fit for purpose.
I am sure it would not cost much to fix but why should the users have to pay out for that. If a fault like this occurs with lots of users after just a few weeks its not just me being heavey handed. Apart from anything if I perform the repair myself and mess it up somehow or round off a screw and then it has to go back to Samsung for a different fault they will not repair it as they will say the device has been previously modified.
I see some people have been asking specifically what is broken. I don't know if this is the same for everyone but it looks like whatever holds to cover to the rubber hinge bit has come off. There is no actual damage such as the rubber being snapped.
I will update when I hear a response from Samsung.
http://i61.tinypic.com/2ns298m.jpg
http://i61.tinypic.com/k1dzrm.jpg
http://i61.tinypic.com/2ns298m.png
http://i61.tinypic.com/k1dzrm.png