All outlets on one circuit read ground hot reversal when tested. Problem started with fan/light going out. I disconnected wires to fan/light; no voltage between black and white. I checked wall switch and ground wire is hot. Is this due to a hot to ground short in one of the outlets or something else?

How did you determine the ground is hot?

It is possible, but not probable, that there is a short someplace causing the ground to be hot, but that would mean that most if not all the equipment grounds in the home are hot, and the equipment grounding system is not grounded properly to allow this condition.

Could be limited to a small portion of the circuit, so as not to affect the entire system.

Used plug in tester. Used wire tester on switch to fan/light. Ground wire shows up hot on all tests just on one circuit.

Ran into this one time, kind of similar. Kind of not.
Went to an attic to do some work, seen a 1/2" metal conduit seperated, (back when conduit was the ground), problem is if a short occurs, one side of the seperation would be live, if a short existed to ground, it would not trip breaker. The other would be at ground potential. and touching both would result in shock or worse. Attics can be cramped. It actually had voltage on conduit, I noticed because of light shock between air ducts and conduit.
It was actually the ductwork was "LIVE" Turned off breakers one by one til duct work was no longer live. Was Central Air circuit. Opened unit and found heat strip shorted to ground, and unit not grounded, causing the air handler to be "LIVE" and ALL Ductwork.
I would check all connections on that circuit. Ceiling and walls. If ground was intact, it should trip breaker.

I Replaced Circuit Breaker- Still Showing Hot Ground Reversal. Went To Work On Dihwasher With Broken Handle And Pushed It Back And Forth. All Of A Sudden Other Circuit Started Working. Could A Short In 220v Dishwasher Somehow Affect The Other Circuit?

A short, or problem with dish washer should not affect affect circuit as they don't share any wires. Could be in the same Box as Dishwasher wiring.
Worse case, disconnect all wires to all affected recepticles, be sure conductors are separated, apply power, see where you have power. Verify integrity of wires between recepticles and any lights. Reconnect.
You have the White wire on the silver screw, right?