I take it that you tried another servo in your servo tester just to verify that it is not the tester itself.
If it is as you expect that the pot is dirty ,or the wiper is not connecting properly then yes it can be cleaned and reset quite easily.
A job for deft fingers I would say, if God has given you sausages for fingers let some one else do the job!
Or as Robbie says trash it. 
Carefully strip the servo apart, checking how it all fits in to the small space inside the servo box. Lay out the gears on a piece of paper and mark how they each fit back in the gear box and on which splines.
locate the wiper pot and carefully unfold the tabs that hold it all together. You are now where you think the problem is. With a clean tissue or cotton bud dipped in switch cleaner (from Maplins) clean all around the area making sure you are not leaving behind any swarf yourself. Check as you put it back together that the wiper spring is in good contact with the carbon track and carefully adjust the spring if necessary.Replace as you dismantled in reverse. and Bobs your dads brother! Or if you have sausage fingers you could send it to me and I will do it for you.
Regards Terry
