There is no way to check a network drive.. the utility must work from the OS that controls the disk. Since that is the TC firmware it is basically impossible.
It is very dangerous to keep your library on the TC disk. very very extremely dangerous. Not only the disk can fail but the TC power supply has known lifespan issue.. at 2-3years.. ironically.
Please backup the TC files now.. right now.. otherwise there is a good chance you won't get them back without a TC rebuild.
But is there a way?
No, you must pull the disk out. It is easy to do.
http://www.ifixit.com/Guide/Replacing-Apple-Time-Capsule-HDD/2750/1
Unless you have applecare there is no more warranty on the TC anyway.. if you have apple care the TC must be purchased no more than 2 years from the date of the computer purchase.
Supposedly they put a heavy duty HD in Time Capsules that should last for 5 Years. I have had mine for 3.
Bolderdash rubbish. The very first TC had an ES seagate 500GB drive.. the vast majority are probably fine.. if the power supply didn't die so fast. No other drive in a TC is more than standard domestic..
Gen 1 1TB is an Hitachi .. might be a bit noisy and runs hot but they are good drives.
Gen 2 1TB is a black WD caviar.. they are dying at a great rate. I have found 2 dead ones so far in TC people have presented me for repair.
All the later TC use a mix of Samsung and WD Green drives.. I doubt yours has one of those, although end of gen 2 they could have changed drives already. WD green drives are same as you buy in the shops.. Latest Gen 4 is WD20EARS.. and I have seen a few dead, and of these not dead but they self delete the format. Leaving all your files high and dry. They are not really a great drive. IMHO. i would never buy one. Use hitachi or samsung at the moment.
http://www.anandtech.com/show/4577/airport-extreme-5th-gen-and-time-capsule-4th- gen-review-faster-wifi-/4
WD staring at you in all its glory.
Ask Apple why they persist with this server grade drive nonsense.. it is based on a standard of MTBF set it 2008 where the Hitachi drive.. (a non-server drive) reached that target. I would like a lot more proof that a standard WD green mets any server standard.. even from 1996.