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.
Not sure about the Mac; on the PC I check using the Ultimate Boot CD and run their drive diagnostics.
I usually tell because when a drive is physically bad, there is a stronger vibration or as the drive resets. There are also log entries about device resets and read/write errors.
If it's a logical error then the drive utilities will normally repair them without further issues (if you repair it, rerun the check and it finds another swath of issues, then again, and again...you probably have a problem physically).
SMART status (also in the disk check utility, but there are some you can get for the Mac for free that monitor it in the menu bar) can give some indication of drive failure as well. The problem with SMART is similar to software memory checkers though; when it says it's bad, it's bad. When it says it's good, it might be bad.
My procedure? If there's a chance that the data in question or giving a problem arose because of something in particular that caused a crash...document corrupted after Word crashes, or bad entries on the filesystem after a hard crash...it's probably filesystem in nature. If there's no rhyme or reason and just failed out of the blue, I suspect it. If it's thunking or giving reset errors in logs, I throw it. If a full defrag of files gives the disk a workout (or a drive diagnostic checking every block) doesn't get it to go spastic, I suspect it's filesystem, not physical drive in nature...
Best Answer
Reformatting any modern hard disk is no different from normal use of the same amount. You cannot actually lay down any track information. Modern hard drives are formatted at the factory using special connectors or special equipment. When you format a modern hard drive, at most you fill the drive with all zeros and maybe map out some sectors that were discovered to be bad.
You will not wear a hard disk out by reformatting any more than normal use will wear it out.
If you are talking about something extreme like continuously formatting a drive, this should be about the same as any continuous read/write access to the drive. You cannot degrade the magnetic medium in any way by doing this, as long as the drive is adequately cooled. A drive that runs at an extreme temperature will definitely have a degraded lifetime.
SSD drives are a different animal where each write gets you closer to eventual failure.