I have dozens of servo motors operating in a project called "Santa's Shop," and one servo joint developed the "jitters" or "shakes." I replaced the offending motor and that restored the operation to normal.
Now that it is summer, I decided to examine the jittery motor and see if I could restore it (as a spare) and I found an easy cure for the shakes.
Remove the four screws that hold the motor shell together.
You are trying to get to the feedback pot, which is usually located beneath the circuit board.
With the board lifted (on my servo), you can see the pot.
Remove the screw that secures the pot.
Locate the tabs that secure the back of the pot.
Using a small screwdriver, bend the tabs so that the back of the pot can be released.
This looked a little worn and dirty, so I cleaned it with a readily available safe cleaning wipe (toilet paper--good for cleaning black stuff). Yes, I wiped it with plain old toilet paper (two ply) for about ten seconds.
I reversed the process and put the servo back together--now it works like new :)