Should the water in the bottom of a dishwasher drain out all the way

Yes it should. If it doesn't and you do not have an air gap check drain hose under sink and be sure it is looped up higher (to the underside of counter) than where it connects to drain or disposal. If tha is all correct, remove washer drain hose from sink and check for blockage. Also check bottom of inside of dishwasher ofr blockage. You may have to remove the screen to check.