So, I don't like the Windows 8 (Store) version of Skype at all. I've found it to be completely unreliable, and it has too many features missing (especially the Send File function). That's unrelated to my problem here, but I just want to explain why I'm using the desktop version on a Windows 8 PC.
With that being the case, I've been trying to get three different Bluetooth headsets I have to work with Skype on the desktop. They ALL work perfectly in the Windows Audio Devices control panel, with both their microphones, and earpiece working. However, as soon as I open Skype (desktop version 18.104.22.168, which has the headset set to be the chosen audio device for both speakers and mic), I hear a beep from the earpiece, and the headset stops working entirely.
Even after closing Skype, all three headsets still don't work. Attempting to play a test tone in the Windows Audio Devices control panel then gives me the error message "Failed to Play Test Tone." This state persists until I reboot the computer entirely.
For what it's worth, this is a desktop-only problem; the WinRT / Windows Store version of Skype has no such problem... it's just near unusable for me for other reasons.
Uninstall the 6.2 version and install the previous 22.214.171.124 version using this msi-installer:
Though I've discovered that Skype isn't fully to blame here. It's triggering this issue, but then, so is putting the Surface Pro to sleep / in S3 standby. Upon resuming, the same thing happens, so there's clearly deeper seeded Bluetooth issues with the implementation on the Surface Pro.