Sensor Issues
 

I have an '04 Mazda 3 (Hatchback) 2.3L.
When cold starting the car, the odometer and speedometer float up and down. Basically until the transmission is warmed up. I have to let the car warm up entirely just to avoid my AT light coming on after the needles floating for so long.
The dash shows it floating between all the gears. From 1 to 3 to 4 to 2 to 1 (it varies). I was told this is the throttle position sensor. But was also told there is another name for the sensor as well.
I need someone to please guide me in the right direction and let me know if this is common with these cars. I have owned this car for four years and it has been so good to me.
Any and all help would be appreciated!