How to replace a drive on the NAS

I had this exact problem on a (tower) server just like you explain, and it was easy:

smartctl will output the serial number of the drive

Vendors sometimes ship their own specific tools, like hdparm, that will do the same.

So output the serial of the bad drive, and then use a dentist's mirror and a flashlight to find the drive.

On a rackmount you'll usually have indicator lights like other people have said, but I bet the same would apply.

When drives are used in an array, the controller will set Time Limited Error Recovery. This will cause disks to report medium errors if they can't immediately read the data. This doesn't mean that they will not recover from the read error, or that the sector is completely unreadable.
_{(Cheap SATA drives do not support TLER, and will cause the read operation to hang while the drive tries to recover the data; this is just one of many reasons cheaper SATA drives shouldn't bused in arrays; this of course doesn't apply to this particular question)}

If the disk determines that the sector is unreadable, it will remap the sector. The original bad sector will not be reported up the chain, so software running on the OS has no way of knowing. The only thing you can do is lookup the SMART report and see if/how many sectors have been remapped. Many sectors being remapped is a good indication of bad things to come. SMART may also report how many times the disk has experience a soft error vs a hard error.

In any case, SMART pre-failure prediction has been less than helpful; a Google SMART Study backs that up.