When I was musing about disk images earlier, I was thinking more about the faults with the disk itself rather than the files. Is it possible to copy the faults from one drive to another like that, effectively harming the new drive, or are the bits and the hardware completely unrelated when restoring a disk image?
The bits and the hardware an image is stored on are unrelated, in the sense you are asking. You can't copy hardware faults between disks. All those "Reported Uncorrectable Errors" though mean that the disk hasn't been able to read a section of the disk and write the files it contains safely to a new location, which is what it would normally do, and then lock out the bad sector that contained the problem. Disk drives fix errors all the time if they have trouble reading files, shown by SMART errors, a failed first read, or some other metric, by moving the files to good locations.
Real disk corruption, of the sort HDS reported to you, would be caused by small hardware failures, probably surface defects on the disk itself. These can be caused by minor bumps while the disk is working, causing the read heads to touch the disk, or particles inside the drive, or temperature issues, etc. Those won't be transferred to a backup disk or the disk you restore it to. But it is possible to copy the errors they create. So a bad sector that can't be read won't be backed up, and the backup software should either report it or fail and stop the backup. A restore of a disk image should also check the format and indexes and report or stop if there is a problem. In fact it should check the image as a first step in the restore process, or the default option should be to do so.
However if a disk has had a glitch at some time, but the sector and the index information about it is still good, then a corrupted file or disk sector can be backed up even to a disk image. Of course the problem will only show itself as file corruption.
On my last data disk failure, a lot of my specific problems were with JPG image files. Pictures I had taken with various cameras over time. I often sorted the directories I had them in by Date taken, which is not a well supported sort in Windows, so the disk got thrashed quite a bit when I sorted that way. At the time I was using the backup function in Norton 360 to do incremental file backups, rather than image backups. That software failed miserably when I tried to do a restore. For some reason the software had lost its record of the backup set, even though the index file containing the information was still there, and I was eventually able to restore most of the data. But it took a lot of intervention from me. Unfortunately Symantec were no help at all, and didn't know the trick I had to use to force the recovery to start, or wouldn't share it.
When I finally did have all but the small amount of lost data restored, I found that more than a few image files had corruption in them. They showed tearing, colour changes and so on in the image, or pieces of the image were in the wrong sequence. So it was file corruption, which had been read from the original disk and backed up to my backup disk. The backup software was verifying the files, so the file was corrupted on the original disk. That sort of corruption will also be backed up to an image, and restored to a new disk. It is the same as a Word document having a few characters changed because of a few bad bits, but the file size stays the same and is readable, just not human readable!
Anyway, good to hear you got it all fixed. Now get some of those drives replaced under warranty!