Error 50 is a generic - iTunes has failed to write a file and the article listing specific store errors (expand the section on Specific Conditions and Alert Messages to reveal -50 in that section) deals with the usual problems where the store is failing or the network is failing.
If the error is bubbling up from the filesystem (or you get the error from Finder), then it's often an "illegal" character in the file or folder name. Look to remove or rename files with emoji, unicode characters or more mundane characters like : & or /
In your case, it's very likely the drive is the cause. You can and should look in the console app to see what other errors happen around that time. Look for I/O errors - disk0 - or just run disk utility and have it verify / repair the catalog file. This will confirm the guess that the drive is failing and the errors are not some software problem.
You could export the current library xml to the desktop and start over with a brand new iTunes library file just to rule out corruption in that file, but then you would have two problems at the same time - terminal unable to write a file and iTunes unable to write a file. Occam's razor (and my experience) says it's the filesystem/drive - not two identical software problems.
Spinning hard drives do track the sectors where a bad write has happened and try to keep track of them so the system won't notice files not vein written, but as a drive ages (or if this mechanism fails) you will get unrecoverable errors more and more.
Also - it's often hard to tell if the catalog structure is bad (which Disk Warrior, Drive Genius and plain old erase in Disk Utility attempt to fix assuming the drive works properly). But if the underlying hardware is failing, you'll need to move to a new drive.
I would just make another backup and zero the drive and look for errors during the zero / reinstall. If the errors persist, it's time for a new drive once the pain of reboots is more than the cost of a new part costs.
In your specific case of an old PPC machine where repair is invasive and the cables likely to be brittle, I would just re-install the OS onto an inexpensive and many GB external drive and run the mac from a cheap USB drive (most iBooks will boot from USB, but not all will) - leaving the potentially failing internal drive sitting unused, unmounted and spun down. It's rare for a failed drive to take down the machine so you can just leave it alone for minimal cost if you can tolerate the iBook running on an external drive.
This question requires additional troubleshooting to pinpoint the problem. But there is probably a bottleneck somewhere.
There are a few things you don't tell us in your question. How are the different computers connected?
- WiFi or Ethernet?
- What speed is the link to the eMac 11/54/100/360/1000 Mbps
- what are the network devices used to interconnect the devices (hubs, switches, routers...)
Make sure all devices have their own sparse bundles on the hard drives.
You should then try to test the different features used during the time-machine backups.
- Test the speed of your hard drives and then during backup monitor the disk usage
- monitor the memory and processor usage on your eMac
- monitor the connection usage (bandwidth)
During the monitoring process try to add more and more macs until you get the errors.
If you see any of these components saturating during the backup you will pinpoint the bottleneck(s).
Best Answer
Try moving the contents of /Library/Receipts somewhere else. I have seen some weird problems caused by corrupted files there a couple of times. Also make sure apps like Little Snitch do not intervene in the process.