Yes, "Error Checking". Select the "Check Now..." button, a windows will appear with two options (or neither option):
Neither option. This should check the integrity of the file system in "read-only" mode (reports problems but doesn't fix).
Automatically fix file system errors. This will check the integrity of the file system and attempt to correct any problems that it finds.
Scan for and attempt recovery of bad sectors. This will scan the disk surface occupied by the file system looking for "bad" sectors. It will attempt to recover the data from bad sectors by moving it to another sector and marking the sector "bad". This option can take a long time depending on the size of the disk volume and should NOT be interrupted. If it finds problems, it can take a very long time to recover (appears hung... isn't... leave it be).
Most people start with just the "Automatically fix file system errors" option to see if that resolves their issue. Neither options may be used when you think the disk drive logic itself is "hosed" and you don't want to risk writing data to the wrong sector. Since yours seems to be able to read some of file system OK, this is probably not the case.
Try not to have open files or use the disk while it's being checked. If the GUI program believes the disk is in use when you request the scan it will probably ask to schedule it at next boot before logon. This should only be necessary for your boot disk (usually logical drive C:).
If your data is really important to you, you should backup/recover as much as you can before messing with the drive, including what I've proposed above. (Standard Disclaimer of Responsibility).