For this type of issues regarding the video when you go to full screen, it's necessary to confirm that your computer meets the minimum system requierements. I also recommend to test it in a different computer, it could be located in a different location, just access Watch at slingbox.com.
I suggest that you try to re-install the plugin on your browser, here is a tutorial that might help,
Well my laptop is brand new (with Windows 7) so requirements are not an issue. I have already reinstalled the plugins for Firefox and Explorer, (but Explorer crashes over and over.) My other two computers, running Windows XP will not find the Slingbox at all using the web browsers so I cannot try the other method.