I have the same video card as well (ATI Radeon HD 6670). I also have a 64 bit system but I am running windows 8.1 ... I am looking for answers as well.
You seem to be having a little bit better luck than me however. I cannot get either the Netflix desktop application working nor the Netflix Metro App to work with these drivers.
When I run either one of them I get a load up of the show and then when it reaches 100% the screen turns to "snow" (snow as in like the old analog TV sets that do not pick up a signal). This snow lasts for about 2 seconds and then the screen goes completely black. Audio still plays though. The only way to recover to my desktop is to close the app or browser down.
I have tried resolving it by running it through different browsers, reinstalling flash, silverlight etc.
To even get it close to functioning...
To get Netflix to play I had to disable the video driver in the device manager. Then it will play. So whatever default driver it reverts to (when I disable it)works but at the sacrifice of my screen resolution and some once in a while artifiacts in my screen. (Not happy about this).
I have tried downloading the old legacy driver and the new generic beta driver. I have not had any luck with either one of these.
My iTunes video playback is suffering as well since all of this.
Have you found any luck in resolving this Netflix issue?