What is probable cause to make transmission skip into overdrive after first and make speedometer reach top speed. 2000 Ford Mustang V6 3.8L engine

check here...

https://www.google.com/search?q=2005+ford+mustang+overdrive+flashing&rlz=1C1CHBD_enUS885US885&oq=2005+ford+mustang+overdrive+flashing&aqs=chrome..69i57j0i22i30j0i390i650l2.6288j0j4&sourceid=chrome&ie=UTF-8

Your best bet , take it to a qualified repair shop. The overdrive off light flashes is telling you that the transmission has a problem an code's are set in the transmission control module or PCM - engine computer . Speedometer an odometer not working could mean speed sensor is bad . Checking code's with a factory or professional scan tool is need . The heater fan not turning off is a seperate problem , relay stuck closed maybe . Is it running at high speed ?

Have you been driving on snow or ice? That will cause this problem.

You don't give me much information to work with. However, 1st, look at the engine mounts. You may have a broken mount. This will make it feel like the transmission is shifting hard. Other than that, there is only a few things that will cause this. The speed sensor tells the computer when to shift the shift solenoids. It may not be "seeing" a quality signal. If this is the case, the speedometer will be bouncing too. Last idea is that it is skipping a gear. Starts in 1st, should go to 2nd at about 10 MPH. 3rd at 25 to 30 MPH. And, if you have a Overdrive transmission, it should go into overdrive at around 45 to 55 MPH. If it is skipping 2nd, it will engage 3rd at a high engine speed, and will feel like a sudden slam into gear. If this is true, your transmission needs some work. Hope this all helps. Good Luck.

1. Reverse order of this
2. Reach up behind the cluster and release the cable by depressing the quick disconnect tab and pulling the cable away.
   
3. Remove the cable from the casing. If the cable is broken, raise the vehicle on a hoist and disconnect the cable from the transmission.
   

Only 1000-2000 RPM? Does it do that in any gear?

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Modern cars no longer use a mechanical cable and speedometer. They have an electronic sensor called the vehicle speed sensor (VSS) which is mounted to the transmission where the old speedometer cable used to go. If the engine was replaced, perhaps the mechanic forgot to plug the wiring harness back into the VSS? Or perhaps he damaged the wiring or the sensor during the engine overhaul. (The transmission has to be removed to remove the engine from the car.)
Charlie

have someone scan it for transmission codes. Most likely it is your Torque Converter that is going out, but it could be a solenoid, What color was your fluid?

Check you speed sensor on the transmission, Overdrive wont work without speed sensor, nor will ABS, or Speedometer.. it all boils down to a speed sensor.

OVERDRIVE ENGAGEMENT IS TIED TO THE SPEED SENSOR SIGNAL, THE SYSTEM WILL NOT GO INTO OD UNTIL THE CAR REACHES A CERTAIN SPEED, IN MOST CASES AROUND 35-40 MPH, THE SPEED SENSOR SIGNAL TELLS THE ECU WHEN THE CORRECT SPEED HAS BEEN REACHED.