It seems that you are having some issues with the Web based SlingPlayer version.
The first issue is related to the encrypted channels. Although the Slingbox gets all of the available channels, it will not show all the digital channels, since they might be encrypted.
Regarding the second issue, you must take into account that the Slingbox PRO HD needs certain connection speed in order to keep a steady connection. The following link will allow you to get the tech specs for the Slingbox PRO HD.