I may be trading for a Blackheart Little Giant Combo and the guy tells me that, "the amp is functioning fine, but in the interest of full disclosure, whenever I play an F on the E string, or a C on the A string there is some sort of rattling or buzzing that I can hear in the background. It's not overpowering or anything, but it is there".

Any idea's what may be the cause of this. I'd like to find out if it's an easy fix, unrepairable, or expensive fix before I make the trade.

it could also be something in the room. different objects resonate at different frequencies. even moving the location of the amp could solve this. if neither that nor switching rooms has any affect then it most likely is a loose screw. preamp tube shields are known for rattling out of place so give that a shot first.
If you don't talk to your kids about GAS, who will?
Yea things can work loose and rattle in an amp. As its a combo the speaker is right there where it can shake everything. Go and check every screw you can find and see how it is.