An error occurred while copying files. The problem may be temporary. If the problem persists, use Disk Utility to repair your backup disk.

I was able to figure this out by digging around in the console after getting the same error. This is how I solved my specific problem:

1. Open Console (Spotlight Search can quickly open this)

2. Click your computer under devices. Typically says "NameMacbookPro"

3. In the search bar type "backupd" without the quotes

4. Run TM backup and let the error occur

5. In Console, look for the an error that looks something like this: Error: (-8062) SrcErr:NO Copying /Users/NAME/Library...

this is the corrupt file that caused my TM error.

6. Locate the file in the location given in console and either delete or backup separately (drag and drop somewhere).

7. Re-run TM and the it should complete the backup

In my case, these steps worked. I hope this helps you.

If you do not find the error message using tyson279 procedure, here are two minor variants that may produce more output.

1) search for "backup" rather than backupd. This may show a few more messages.

2) after step 4, select the first console message of the start of that Backup. Then delete the search string so that you can see ALL messages from that point, and look again (starting at the line you selected) for that error message.

The late James Pond saw this problem and wrote a pleasant illustrated article about it:

.Pondini's Time Machine - Troubleshooting: C3. ". . . an error occurred while copying files . . ."

.

If you can back up another Mac to the Time capsule, that means the problem is on your Mac, not the backup device.

You can run Disk Utility Repair/First Aid on your Mac's drive to check for Directory problems.

As it says in James Pond's article, the problem is often limited to One single file that is being difficult.

..and when you follow the recommended procedure in James Pond's article, what error messages are you seeing in Console when you attempt to copy from your Mac to the Backup drive?