Same problem here on a Samsung BD-J5900 which I received less than a week ago. I set it up on Thursday night and the Opera store worked fine (but no iplayer or ITV hub or All 4 - so pretty poor - but at least iplayer is meant to be coming). But today after "Browser initialising, please wait..." for a second or two it then displays a picture of a TV with a line through it nd a message saying "We are sorry but your device is not supported (err:496)." Worse still if I then just press Exit on the remote the whole box freezes and the only way to get it back is to unplug it. The workaround appears to be to press Return before Exit - but I'm not sure if that's always the case. As for the amazon store - many times the box never gets past the initial loading g message and then I just have a black screen. But other times it does work.
I have a wired ethernet connection and the network settings are always good. I'm on the latest firmware. So it seems that this Opera TV Store and it's apps are flakes at best.
It would be nice to get a response from someone from Opera...