Many times when working on the cooling system of these vehicle's air can be come trapped in the system causing conditions similar to the one you are describing. The mechanic may want to try to bleed the air from the system to see if this resolves the problem. The coolant light could be caused by a faulty coolant level sensor. This is considering there are no leaks in the system.
The mechanic has bleed the system twice after performing work on the vehicle. He just did it after replacing the thermostat. We both have not seen any leaks. He did a pressure test of the system and did not find any leaks or drop in the pressure.
I don't believe the gage is faulty. I can suggest a full system flush. If you don't have any other ideas of why the car is sometimes blowing cold air and overheating then I will accept your answer.Thanks