Recently, running Update Manager in Linux Mint 13 (a variant of Ubuntu Precise Pangolin) gave a number of errors.
The listed errors took the following form:
W: GPG error: http://archive.canonical.com precise Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <email@example.com>
A solution, found on Ubuntu Forums, was to rebuild the package cache using the commands:
sudo mv lists lists.old
sudo mkdir -p lists/partial
sudo apt-get update
Once these commands had been implemented in Terminal, Update Manager ran normally, with no errors.
[SOLVED] Package Manager & Update Manager problems