I have the exact same problem on Windows 7 (64-bit).
I too have Flash 10 installed.
Each time I laungh SlingPlayer I get the "Library Not Registered' error.
Yet, my slingbox seems to work just fine.
It seems to imply something needs to be reregistered? Is this a COM components that failed to register?
I'm running IE 9.
Can SOMEONE from Sling please address this problem?
On a related note, if you encounter the error "Slingbox Setup Assistant Requires Adobe Flash Player 8..." when running the Slingbox SlingPlayer Setup Assistant, go into Internet Explorer's Security setting and add the IP address of your Slingbox as a Trusted Site, which will give permission to allow Adobe Flash Player and the SlingPlayer's ActiveX controls to run for the Slingbox's IP address.
IOW, open IE, click Tools, Internet Options, Security, Trusted sites, Sites, type the IP address of your Slingbox (for example, 192.168.1.10), uncheck the box "Require server verification (https:) for all sites in this zone", and click Add, Close, Ok.
Now, exit SlingPlayer and re-open it and run the Setup Assistant. Hopefully, the error will have magically disappeared!
One other tip: Since it can be difficult to determine a new Slingbox's IP address before Setup Assistant has configured it, go to www.SysInternals.com and download TCPView and run it on the same PC on which Setup Assistant is running and look for the line that shows SlingPlayer.exe and a Remote Address of an IP address on your LAN immediately followed by :5001, for example 192.168.1.10:5001. The IP address you see is your Slingbox's IP address which you'll enter as a Trusted Site.