I have a 1978 corvette and the speedometer is not accurate and jumps around lot. any idea what is wrong with it.

For all 1978 Corvettes, the location of the Vehicle Identification Number (VIN) is stamped on a plate attached to the left front body hinge pillar.

buy a haynes manual at a partplace

sounds like your in the area could be a bad sensor or a bad wire that your moving around when changing the sensor

check speedo cable for tightness at both ends,1 on trans 1 back of dash.if tight replace the cable,they can bind or strstch in liner causing speedo bounce.

Those are vacuum actuated headlights and the vacuum leaks down when the engine is off. Probably have a leak in the headlight actuators, will need to replace or rebuild one or both of them, not a big problem for them to pop up some people just do not like for them to pop up while parked.

Possibly a bad ground wire at the sender on the tank,

Check for that first before tearing into the dash to replace the guage.

REmove speedo cable & inspect inner cable for frayed wire. If not frayed lube cable with graphite grease preferably or oil. replace cable. this should solve problem. If not replace cable.

Well it sounds like you've started to do your "due diligence", but there are several things left out. Your problem could be many things. Something as minor as a vacuum hose left off, loose, or in the wrong place. And just because you changed the plugs and wires, don't mean you fixed your problem. Open your hood at night and see if you have any sparks "dancing" around. Another way to check this is to open your hood and spray a soapy water solution on your plug wires and look for sparks jumping around. If so replace your wires. You didn't mention what type of wires and plugs you used. I would reccommend NKG platnum plugs and a Bosch wire. I know this from experience,(the hard way teacher). It could even be the gas you are burning. I've owned a lot of Vettes, and I am the kind of guy who believes they should be driven. If not it's like having a beatiful wife and never taking her to bed.I know a lot of people who only drive them "once in awhile". Sitting in thier garage can cause many fuel problems, condensation, sludge in the carb, or filters etc. This can all lead to the problem you are describing.
Low speed miss- usually plugs
High speed miss- usually wires or valves
intermitten miss, fuel or electrical.
I hope I gave you some places to look to find your problem.

bad ignition switch

speedometer works intermitently