BMW: 1989 bmw 325ic radiator replacement, coolant level, radiator replacement

Question
I had my radiator replaced this week, now the gauge on the dash goes crazy up/down.  I have heat when i am driving but not heat when I am at idle.  The mechanic changed the sensor and also the thermostat.  i don't know if he bled the system but am very dissapointed in his work.  Can you think of anything i might be missing so I can troubleshoot this.  It cost me a lot of money for all of his work.  Also I when I drive on the highway I am hearing a whiring noise coming from the rear of the vehicle.  I had changed my differential fluid two months ago hoping it would help but the whiring noise is still there.  Thirdly, I have a leak in my trunk that I thought was from the third light but can't fix it.  Water gets into trunk everytime it rains. Thanks for any help you can give.

Answer
Greg,
 The gauge may or may not be reading correctly.  These gauges are known to be faulty and are one of the aggrivating problems with these cars.  So the gauge bouncing irratically is likely a connection problem, however the "no heat at idle" is disturbing.  The next time the gauge is bouncing around, press on the cluster or tap on it and see if it fixes the problem temporarily.  If it does, then you KNOW that the problem is electrical.
 Is the coolant level low?  I would let the car sit and cool down, this should give the thermostat time to close.  With the engine cold, start it up and open the coolant reservoir and wait.  You should watch the coolant for any signs of movement.  after a few minutes (depending on outside temperature) you should start to see warm coolant flowing back into the coolant reservoir.  If the coolant is low in the tank, or there is no movement, then you have a problem.  If you open the reservoir and see movement immediately then your thermostat is stuck open, and thats why you cant get any warm air at idle (the engine cant warm the coolant)
 The whining noise you hear is likely a rear wheel bearing.  Good call on changing the fluid, but it's more likely to be a problem with the wheel bearings.
 The leaky trunk is from at least one seal that's bad.  The 3rd brake light "could" be the problem, but its more likely to be a tear or hole in the weather strip that seals between the trunk lid and the body.  Also its possible to get water in through the tail lights.  There is a foam gasket that sits between the body and the tail lights and this leaks from time to time.

 Good luck,
 Josh