A whole slew of updates have appear for my Linux Mint Debian Edition PC. However, to instate them, I needed to remove VMware Player and this is the command to do so:
sudo vmware-installer -u vmware-player
It worked in my case and my system updates are in progress as I write this. The same command should work for other Linux distros where VMware Player was installed using the *.bundle installer. VMware Player remains in place on my main PC though so I am not ditching it just yet, even if I have to be careful when running it on Linux Mint 13 so as not to freeze the system on myself.