I have a red warning sign in my toolbar. When I click on it, it asks me to check for updates. When I check for updates, I get this:
W:Failed to fetch http://dl.google.com/linux/deb/dists/testing/non-free/binary-amd64/Packages 404 Not Found [IP: 74.125.227.46 80]
W:Failed to fetch http://dl.google.com/linux/deb/dists/testing/non-free/binary-i386/Packages 404 Not Found [IP: 74.125.227.46 80]
E:Some index files failed to download. They have been ignored, or old ones used instead.
This happened to me once before when 12.04 was still in beta, but I can't remember what I did. It was a huge mess!
System:
12.04 64-bit
Sony Vaio VGN-NW220F
It looks like you (or a piece of Google software) added a Google repository that is no longer valid. This shouldn't prevent you from updating the rest of the system.
Whatever that Google repository was, it's gone now. If it was a PPA, you can try removing/unchecking it in Software Sources. If you added those lines manually to sources.list, remove and run sudo apt-get update.
Found a mirror of that site here: http://aptproxy.linuxdeepin.com/dl.google.com/linux/deb/dists/testing/non-free/binary-i386/
Looks like it contained the apt repo for Picasa, which Google has officially discontinued for Linux. Hence they pulled the plug on the repo itself. Would have been nice if they simply left it up, but then again, this way you know it's gone and can move on (to the Windows Wine version).
Not really a perfect answer, but I reinstalled Ubuntu in a clean upgrade.