How much free space is there on your main drive (the one you are backing up)? Low free space can prevent backups because Time Machine needs some space on the main drive to arrange things. This can be made worse if you don't run Time Machine frequently, or if there are large gaps in time between your backups.
Other possibilities: do you have "app cleaner" or Clean My Mac type software/utilities on your Mac? They have been implicated in some instances of the error messages you are getting.
How is your external drive set up? Do you use Disk Utility to set it up, or did you use proprietary software tools/firmware from the external drive manufacturer?