Time Machine Dementia

[bayswater]

Now and then, Time Machine reports that there have been no backups for 438 (or similar) days. Opening TM shows all the backups that should be there, and that they are usable to restore deleted files. TM appears to confuse the date of the first backup with the date of the last backup.

More recently, TM has sporadically reported that the backup disk is nearly full. In fact the backup disk has 1.7G of 2.0G free.

Is there some way to reset TM so it knows what it's doing, knows what disk it uses, and remembers what it did an hour ago?