Servo wandering and jitter are common problems which develop in servos with use over time, and this problem can often be repaired without necessitating the replacement of the servo.

The servo consists of some control circuitry mounted on the circuit
board, a motor which provides movement, a gear train which multiplies
the torque of the motor, an output shaft which is the output of the
servo, and a feedback potentiometer. The feedbak potentiometer is a
device which tells the control circuitry where the output shaft is, so
that it can tell the motor which way to go to make the output shaft be
where it is supposed to be. Servo jitter and servo wander are most often
caused because of a dirty or worn potentiometer. The output shaft of the
servo is supported by a bearing -- cheap ones by a bushing type bearing and
expensive ones by a ball type bearing. A worn output bearing may cause
output shaft wobbling which can only be solved by replacement of the
bearing. This wobbling can also contribute to servo wandering due to
movement of the feedback potentiometer input shaft.

To rectify the problem of jitter, the servo must be disassembled, the
potentiometer removed, and taken apart. In order to do this, first the
case must be taken apart, and then the motor and circuit board removed.
The potentiometer is sometimes affixed directly to the circuit board, in
others the potentiometer will be attached with lead wires. It is most often
affixed to the case with a small screw. On some servos, removing this
screw will enable the potentiometer to be removed, and on other servos
this screw holds the back of the potentiometer onto the front of the
potentiometer, thus disassembling the pot. Once it is removed, it must be
disassembled (if not already done) -- they are normally crimped together
with three tabs. Once two of the tabs are bent back, the top of the
potentiometer should come off. Note the orientation for ease of future
reassembly.
If you've followed the steps so far, you'll note that the potentiometer is of the carbon type, not the cheaper wire wound type. This is because only the carbon type has the required resolution for precise servo positioning. You will note that there are some small fingers which form the wipers on the potentiometer, and these contact the carbon on the other half of the potentiometer. Often in older servos, these wipers will wear completely through the carbon, making for a poor contact. If they are bent slightly so that they ride on fresh carbon, good contact can be restored. Since everything is apart anyway, it is a good idea to clean the carbon surface if it shows any sign of crud on it at all.
To re-assemble, just put the potentiometer back together (being careful not to damage the wipers), crimp it or install the fixing screw, and then put everything back together. Everything should be able to fit pretty much only one way.
Servo reversing is accomplished by reversing the power wires to the motor and by reversing the two outer leads on the potentiometer. Some servos use wires to attach the control circuitry to the motor and the potentiometer -- these are easy to change. Other ones mount the motor and potentiometer directly to the circuit board -- these are more difficult to change. If this is the case, then the motor can be unsoldered and rotated 180 degrees, and the potentiometer leads can be cut and new wires spliced in which cross the outer leads.
Or, you could build this simple servo reversing circuilt.