Are you only seeing the error with one particular file, or does it happen with every file?

'Disk Problem' has been around for ages & I don't think there's ever been one fix that works for everyone.

Defragmenting the HDD has worked for some people - give that a try first.
Changing download location worked for me - downloading to an external drive fixed my prob in an older version.
Are you using the default saving location (C:\Documents & Settings\username\My Documents\LimeWire\Saved)?
Are you using Vista? If so, do you have an administrator account?

You could try deleting LW's preferences folder when LW's properly closed. See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will change all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.
In case you're using Vista: LimeWire Pref Folder in Vista

These threads are very old but might have something to help.
The "disk problem" problem
Disk Problem??
disk problem
Low Disk Space Message