2001 Jeep Grand Cherokee Automatic Transmission Starts In Third Gear Sometimes And Somtimes Gets Stuck In Second Gear. Fluid Level Is Fine. What Is The Cause?

You have a Chrysler transmission in your jeep, which is known to have sensor problems.
  Such as; input or output sensors.
 If your speedometer is not working properly, neither will your transmission, (as an example).
From your description, it sounds more like an electronic issue, rather than a mechanical problem.