Time Machine Drive Failure
I would suggest using rsync, which will sync all files and folders from a particular directory to another and skip over files it can't transfer because of damage. Use the following command to copy the entire root directory of your current Time Machine drive to a new drive:

sudo rsync -avxr --progress /Volumes/BadDrive/ /Volumes/GoodDrive

Due to the damage, you probably won't be able to continue using the new drive as a backup drive. It's likely that rsync will skip over some damaged files, causing OS X not to recognize it. 

Another option would be to attempt to use Drive Genius to repair the existing drive. However, this probably won't work with an invalid node structure.

You could also use SuperDuper! to copy the existing files over to the new drive. However, you may run into the same problem as rsync in that it may not preserve the Time Machine file structure.

Good luck.