Does Skype video work on a Samsung Galaxy 10.1?
The official Skype app currently does not support video on NVIDIA Tegra 2 chipsets, according to their FAQ:


  * This specifically does not include some tablets that use the Tegra 2 chipset (e.g. Android tablets and Motorola Atrix do not support video calling).


From what I read on various forums, a test version that does work on Honeycomb tablets sporting Tegra 2 has been seen floating around in Youtube videos, so it should be coming to official channels shortly.