As you can see, the drive's power-on hours are 520 (which is accurate, as I've had it for under a month), but the two errors say they occurred at 10610 hours and 16878 hours — obviously impossible.

What's happening here? Are the errors real? Worrisome? Could there be some kind of "odometer tampering" going on here by my vendor? //

I think that your suspicion of "odometer tampering" is correct, and it is possible. The recorded errors are likely real and definitely worrisome because they indicate bad sectors upon reading. The disk was likely wiped before making its way to you, so those bad sectors have probably been remapped.

Whoever sold you the hard drive reset the S.M.A.R.T. attributes to make it look like a new hard drive.
Anecdote

On 25 July 2015, I purchased six very similar hard drives from goHardDrive.com. When I checked all the disks, I experienced almost the exact same symptoms: