I'm using Ubuntu 64 bit 12.04.3 LTS. About a week or so ago, I noticed that when Update Manager runs (which I do pretty much every day) it no longer says "The package information was just updated." after I do the "Install Updates" - it now says "The package information was last updated # days ago." The # is now up to 7. This is even though I have successfully downloaded and updated a number of things over the past week.

Today, for the first time, I began seeing a warning icon at the upper right of the screen (the red triangle with the exclamation point in it); when I click on that it displays the message "The update information is outdated. This may be caused by network problems or by a repository that is no longer available. Please update manually by clicking on this icon and selecting 'Check for updates' and check if some of the listed repositories fail."

When I do the "Check for updates" as it asks, the warning icon goes away for a bit, but soon returns. I couldn't see any message about any repositories failing.

So: I went to a terminal and ran "sudo apt-get update"; everything went as expected, but i got the following warnings at the end:

[FROM TERMINAL:]
W: A error occurred during the signature verification. The repository is not updated and the previous index files will be used. GPG error: http://extras.ubuntu.com precise Release: The following signatures were invalid: BADSIG 16126D3A3E5C1192 Ubuntu Extras Archive Automatic Signing Key <ftpmaster@ubuntu.com>

W: Failed to fetch http://extras.ubuntu.com/ubuntu/dists/precise/Release

W: Some index files failed to download. They have been ignored, or old ones used instead.
END [FROM TERMINAL]

I did find a similarly named thread, but it didn't seem like the same symptoms, so I posted this separately.

So: what does this mean? and, more importantly, how do I fix this?

Thanks.