Needle bounce is generally a symtom of a dry and/or kinked cable. They used to make some stuff called "Cable-Ease" or something like that which was basically 10 weight oil and graphite. Worked great and stained anything that got even close to it.
Once you have the cable clean and lubed up determine the error in your ODOMETER. That is, make sure it records the number of miles traveled accurately. I used to use 10 mile posts on the freeway to check (before I got a GPS). 10 miles makes it really easy to see how many percent off you are. If it's off, change the speedometer drive pinion in the transmission to get the odometer accurate. This should have the speed indicating pretty close, but if not there are several speedometer shops nation wide that can adjust the instrument itself.