Time Machine is a life saver. I was backing up a machine recently and error was thrown. Indicated in a form like this message (this message occurs on a machine running Lion and I am running Snow Leopard 10.6.5).
Due to the suggestions by James Pond , I found that there was a widget called Time Machine Buddy . I downloaded the widget and it told me what the offending file was. I deleted the file and happily backed up the rest of my drive. I don’t know what caused Error 11 or exactly what that is but, the deletion of the file, which was not crucial to keep, allowed me to continue.