OK, after doing some research, I think this error is probably related to having been rooted. What is your flash counter at? You can check by booting into download mode. If it's not zero, the factory update.zip isn't going to work. Also check device status: Settings / About device, then scroll to the bottom of the page. Is Device status normal, or modified?
If these aren't 0, and normal, update.zip won't work. You may need to root again, apply the update manually, and then unroot if you really don't want to be rooted.
I would strongly suggest this process for rooting:
http://forums.androidcentral.com/sp...e-updated-how-root-your-sprint-galaxy-s3.html
Then post #2 of this thread for updating:
http://forums.androidcentral.com/sprint-galaxy-s-iii/272331-your-way-update-md4.html
Why did you unroot? You can stay on the stock ROM while rooted, so in my opinion there's really no need to unroot unless you're returning the phone to Sprint or Samsung for service.
But if you want to unroot, go here:
http://forums.androidcentral.com/sp...-30-2012-sprint-only-unroot-return-stock.html
If you're going to unroot, be sure to read that entire thread. Part way through, in post 451 there's a newer ROM than the one in the OP. I'd use that one. Note that after unrooting you may not be on the most current ROM, in which case you'll have to apply the OTAs to get current. But at least the OTAs will work.