Unable to find index entry in index ID 1, of table {object_id of table}, in database 'msdb'. The indicated index is corrupt or there is a problem with the current update plan. Run DBCC CHECKDB or DBCC CHECKTABLE. If the problem persists, contact product support.I found this blog post and the script in it repaired the msdb.
(The command that fixed it is DBCC CHECKDB('msdb', REPAIR_REBUILD), but there is quite a bit of preparation that needs to be done before this command will execute successfully. See the blog post I referred to.)