How to back up "The disk has S.M.A.R.T. errors"

[hicsuntdrac0nis]

My computer won't start up past the login screen so first i tried Safe Mode [Shift+Start up] didn't work . Then I tried to reinstall software [Command+R+Start Up] my apple logo turned into a circle with a line through it and the gear never stopped spinning [about half hour later] so I turned it off. I then tried to reset the NVRAM [Command+Option+P+R] and I got to a screen that said "Mac OS X Utilities" from there I went to Disk Utility and saw that my disk had S.M.A.R.T. errors. I clicked "Repair Disk" and it found the problem and fixed it apparently. However, when I tried to reinstall Lion I got this image

So I have a few questions:

If my disk is corrupted, why did it say the repair worked ?
If my disk is corrupted, how can I back up the files if I can't login ?
Is it possible to repair the S.M.A.R.T. errors ?
I want to AT THE VERY LEAST back up my photos and a few documents, is there any way I can put those files onto a USB through Disk Utility ?

Thanks in advance

 

[chrfr]

SMART errors mean the disk is going to fail imminently. You need another disk to work from, and it is possible that you won't be able to recover your files at all if you don't already have a backup.

 

[MisterKeeks]

Firewire boot disk mode?