Gail, I don't know what the problem was. It seems to have gone away when I ran the backup successfully. As I said, that step includes a "reorganize index" step, so maybe that fixed the indexes. The error file had:
Error: 2013-05-09 14:50:40.63
Code: 0xC0024104
Source: Reorganize Index
Description: The Execute method on the task returned error code 0x80131501 (An exception occurred while executing a Transact-SQL statement or batch.). The Execute method must succeed, and indicate the result using an "out" parameter.
End Error
Which I (not knowing what I'm looking at...) interpreted as a separate error.
Jim