I used the following to correct the inverted video in Skype 18.104.22.168 (Beta) problem on my Asus UL30A notebook w/ Ubuntu 12.04 64bit. This notebook shipped w/ a Suyin Corp. Asus Integrated Webcam [CN031B]. The video was not inverted in Cheese.
1. Rename /usr/bin/skype to /usr/bin/skype.original.
2. Create a new /user/bin/skype file.
sudo mv /usr/bin/skype /usr/bin/skype.original
3. Paste the following:
sudo gedit /usr/bin/skype
4. Save & exit gedit.
5. Make /usr/bin/skype executable.
6. Start Skype as you normally would.
sudo chmod +x /usr/bin/skype
I can't take credit for this solution. I found it via google except the path to v4l1compat.so was incorrect in the other solutions I found.
Hope this works for you if you have a similar problem. Comments welcome.