Every time I restarted Skype it promised a new release of 6.0 that it would download but then fail to update:

Skype was unable to install the update because the old application can’t be overwritten.

Pretty unhelpful error message.

It was an ownership problem: I finally found the solution today in this thread in the Skype forum:

1. Open terminal

2. sudo bash

3. ls -l /Applications

    check which non root owns most apps (third column)

4. ls -ld /Applications/Skype.app/

    check which user owns the Skype app

5. If Skype.app is not owned by the usual user then

    chown -R whateveruser /Applications/Skype.app/