Yes.
I stopped the backup. Removed spotlight indices from both drives, and ran Disk Utility on the TM sparsebundle.
Disk Utility announced that it could find no errors with the TM disk.
Spotlight started indexing---and estimated 5 hours to do the job on the main disk. (I don't know if it took that long, I went to bed before it finished with 2 hours estimated to go).
I started up TM again.
16/08/11 7:44:11.774 AM com.apple.backupd: Starting standard backup
16/08/11 7:44:11.776 AM com.apple.backupd: Attempting to mount network destination URL: afp://x@y._afpovertcp._tcp.local/Wells-3
16/08/11 7:44:12.460 AM com.apple.backupd: Mounted network destination at mountpoint: /Volumes/Wells-3-1 using URL: afp://x@y._afpovertcp._tcp.local/Wells-3
16/08/11 7:44:33.978 AM com.apple.backupd: QUICKCHECK ONLY; FILESYSTEM CLEAN
16/08/11 7:44:37.349 AM com.apple.backupd: Disk image /Volumes/Wells-3-1/xxx.sparsebundle mounted at: /Volumes/Time Machine Backups
16/08/11 7:44:37.366 AM com.apple.backupd: Backing up to: /Volumes/Time Machine Backups/Backups.backupdb
16/08/11 7:44:40.365 AM com.apple.backupd: 88.76 GB required (including padding), 423.38 GB available
16/08/11 7:44:40.425 AM com.apple.backupd: Waiting for index to be ready (100)
16/08/11 7:49:18.608 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 131, length 7, native = no)
16/08/11 7:49:22.503 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 131, length 7, native = no)
16/08/11 7:49:41.002 AM com.apple.backupd: Copied 16120 files (0 bytes) from volume H.
16/08/11 7:49:41.002 AM com.apple.backupd: Event store UUIDs don't match for volume: H
16/08/11 8:44:40.487 AM com.apple.backupd: Copied 101.5 MB of 74.0 GB, 541750 of 3687840 items
16/08/11 9:44:40.784 AM com.apple.backupd: Copied 263.7 MB of 74.0 GB, 913868 of 3687840 items
16/08/11 10:43:13.359 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 131, length 7, native = no)
16/08/11 10:43:13.359 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 132, length 7, native = no)
16/08/11 10:44:43.289 AM com.apple.backupd: Copied 274.4 MB of 74.0 GB, 1179865 of 3687840 items
16/08/11 11:36:48.297 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 128, length 7, native = no)
16/08/11 11:36:49.345 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 133, length 7, native = no)
16/08/11 11:36:50.845 AM mdworker: iCal.mdimporter: could not find component keys: /Users/michaeln/Documents/Calendar Backup/Calendar.ics
16/08/11 11:36:51.125 AM mdworker: iCal.mdimporter: could not find component keys: /Users/michaeln/Documents/Calendar Backup/Library Loans.ics
16/08/11 11:37:13.675 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 128, length 7, native = no)
16/08/11 11:37:59.078 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 132, length 7, native = no)
16/08/11 11:37:59.179 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 128, length 7, native = no)
16/08/11 11:38:00.688 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 128, length 7, native = no)
16/08/11 11:38:00.689 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 129, length 7, native = no)
16/08/11 11:38:00.970 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 129, length 7, native = no)
16/08/11 11:38:01.345 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 129, length 7, native = no)
16/08/11 11:38:50.344 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 129, length 7, native = no)
16/08/11 11:38:53.402 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 131, length 7, native = no)
16/08/11 11:39:01.823 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 128, length 7, native = no)
16/08/11 11:39:02.206 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 128, length 7, native = no)
16/08/11 11:44:43.320 AM com.apple.backupd: Copied 382.9 MB of 74.0 GB, 1362117 of 3687840 items
16/08/11 12:44:44.153 PM com.apple.backupd: Copied 497.5 MB of 74.0 GB, 1523970 of 3687840 items
16/08/11 12:59:41.330 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 128, length 7, native = no)
16/08/11 12:59:53.541 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 131, length 7, native = no)
16/08/11 1:00:00.529 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 131, length 7, native = no)
16/08/11 1:28:51.989 PM com.apple.backupd: Copied 1679760 files (716.8 MB) from volume C.
16/08/11 1:28:51.990 PM com.apple.backupd: Event store UUIDs don't match for volume: C
16/08/11 1:28:52.002 PM com.apple.backupd: Waiting for index to be ready (100)
[snip 60 lines]
16/08/11 2:48:05.251 PM com.apple.backupd: Waiting for index to be ready (100)
16/08/11 2:48:47.151 PM com.apple.backupd: Copied 716.8 MB of 74.0 GB, 1679760 of 3687840 items
16/08/11 3:48:49.712 PM com.apple.backupd: Copied 821.0 MB of 74.0 GB, 2204398 of 3687840 items
16/08/11 4:51:37.955 PM com.apple.backupd: Copied 821.0 MB of 74.0 GB, 2449918 of 3687840 items
16/08/11 5:51:38.857 PM com.apple.backupd: Copied 821.6 MB of 74.0 GB, 2550272 of 3687840 items
16/08/11 7:53:08.202 PM com.apple.backupd: Copied 821.7 MB of 74.0 GB, 2616564 of 3687840 items
16/08/11 9:19:47.726 PM com.apple.backupd: Copied 821.7 MB of 74.0 GB, 2741313 of 3687840 items
16/08/11 10:23:22.682 PM com.apple.backupd: Copied 821.7 MB of 74.0 GB, 2755541 of 3687840 items
16/08/11 10:35:35.644 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 128, length 7, native = no)
16/08/11 10:35:37.166 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 133, length 7, native = no)
16/08/11 10:35:37.666 PM mdworker: iCal.mdimporter: could not find component keys: /Volumes/B/Users/michaeln/Documents/Calendar Backup/Calendar.ics
16/08/11 10:35:38.412 PM mdworker: iCal.mdimporter: could not find component keys: /Volumes/B/Users/michaeln/Documents/Calendar Backup/Library Loans.ics
16/08/11 10:35:55.223 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 128, length 7, native = no)
16/08/11 10:38:05.508 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 132, length 7, native = no)
16/08/11 10:38:05.752 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 128, length 7, native = no)
16/08/11 10:38:06.963 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 128, length 7, native = no)
16/08/11 10:38:06.963 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 129, length 7, native = no)
16/08/11 10:38:07.488 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 129, length 7, native = no)
16/08/11 10:38:08.200 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 129, length 7, native = no)
16/08/11 10:39:01.155 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 129, length 7, native = no)
16/08/11 10:39:07.542 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 131, length 7, native = no)
16/08/11 10:39:11.270 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 128, length 7, native = no)
16/08/11 10:39:11.880 PM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 128, length 7, native = no)
16/08/11 11:23:23.059 PM com.apple.backupd: Copied 821.7 MB of 74.0 GB, 2879773 of 3687840 items
17/08/11 12:06:02.717 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 128, length 7, native = no)
17/08/11 12:06:32.642 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 131, length 7, native = no)
17/08/11 12:08:13.527 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 131, length 7, native = no)
17/08/11 12:23:23.466 AM com.apple.backupd: Copied 821.7 MB of 74.0 GB, 3013165 of 3687840 items
17/08/11 12:36:20.110 AM com.apple.backupd: Copied 3047162 files (903.9 MB) from volume B.
17/08/11 12:36:21.083 AM com.apple.backupd: Event store UUIDs don't match for volume: B
17/08/11 1:23:24.259 AM com.apple.backupd: Copied 2.4 GB of 74.0 GB, 3205007 of 3687840 items
17/08/11 2:25:03.373 AM com.apple.backupd: Copied 8.8 GB of 74.0 GB, 3400703 of 3687840 items
17/08/11 3:25:03.921 AM com.apple.backupd: Copied 10.9 GB of 74.0 GB, 3418528 of 3687840 items
17/08/11 4:25:54.486 AM com.apple.backupd: Copied 13.0 GB of 74.0 GB, 3456877 of 3687840 items
17/08/11 4:48:17.957 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 128, length 7, native = no)
17/08/11 4:53:41.988 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 129, length 7, native = no)
17/08/11 4:54:15.109 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 129, length 7, native = no)
17/08/11 4:54:15.882 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 129, length 7, native = no)
17/08/11 4:54:21.488 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 129, length 7, native = no)
17/08/11 4:54:27.574 AM com.apple.backupd: CoreEndianFlipData: error -4940 returned for rsrc type FREF (id 129, length 7, native = no)
17/08/11 4:56:07.472 AM com.apple.backupd: Copied 3489710 files (30.5 GB) from volume E.
17/08/11 4:58:49.440 AM com.apple.backupd: Waiting for index to be ready (100)
[snip 840 lines]
17/08/11 7:34:40.606 PM com.apple.backupd: Waiting for index to be ready (100)
So, no, that didn't work in any meaningful way at all.
I've stopped it again. Then I'll install the latest Lion upgrade, in a clutching-at-straws hope that it fixes something.