Repair permissions is generally unneeded and considered to be voodoo. You see it bandied around the forums a lot here, as some kind of universal solution to misbehaving hardware/software/solar flare activity.
In reality, it's an old legacy feature from back in the day when you could dual-boot OS X and OS 9 on the same Mac. OS 9 had no concept of unix-style file permissions, and it could occasionally muck up the permissions on OS X HFS+ filesystems. Running "Repair Disk Permissions" just resets file/directory permissions to match their initial settings. Each app you install via a .pkg file leaves a .bom (bill-of-materials) file in /var/db/receipts. Repair permissions looks at each of those receipts and resets the application's file permissions accordingly.
The thing is that some applications do change their file permissions after they've been run. Or, you may have a valid reason for changing them yourself. I've seen instances where "repairing" permissions actually broke things by denying access to shared files.
The problem is in the wording. "Repair" implies that something is broken, and isn't repairing always a good thing to do? Reset file permissions might be a better wording.
In any case, if you aren't installing applications via .pkg files to the external drives, you definitely don't need to bother w/repair permissions ... and if you are installing apps there, you probably *still* don't need to bother with it.
Source: worked as an Apple tech and unix sysadmin for a very long time, and I am one with disk permissions
But if you don't believe me, here's John Gruber's take on it:
http://daringfireball.net/2006/04/repair_permissions_voodoo