I have exactly the same problem and the suggestion of enabling video calls from the menu has no effect. Strangely I have exactly the same issue with my mobile phone - a Samsung Galaxy S II - which, like the Sony Tablet, is running the most recent Skype software and Android 3.2. With both machines I can make audio calls, but not video calls and in both cases the video is enabled up until the moment the recipient answers. Oh, and it's not a problem with my laptop, just in case you thought I couldn't work Skype.
Any help with this would be most gratefully received.
Yeah and maybe finally you will repair voice on your skype. I has video but voice is like half duplex and its really bad. I checked with few of my friends and always the same. Voice is very weak like from another room. Maybe u will put on the your soft something like in PC version (audio options and boost of mic), because now it's nightmare to call to someone.
I now can see people when I skype but they cannot see me. Video is enabled in the settings. On the screen I can see the small camera icon with a slash through it and I can go through the steps to select the front camera, but nothing changes.
When I got my tablet, the skype that it came with didn't work with video calling. I tried the system update but that doesnt fix the problem. If you uninstall skype, then download it from the app store, and install it, it will work! at least for me