The first thing that I would check is the drain. Make sure that it’s not blocked, preventing the wash water from draining prior to the rinse cycle. If there’s too much wash water left, then the sprayer bar may be trying to turn through undrained water instead of spinning freely in air. That would prevent a proper rinse, which seems to be what you’ve described. (It sounds like the wash is working more or less okay.)
There should be a drain plate in the machine, with either a basket trap or a drilled plate. Make sure that there’s nothing blocking that. If that’s not the problem, then there could still be a problem with the drain hose, which generally runs upward and then downward into your sink’s P-trap. (Since you haven’t mentioned a problem with the P-trap or the sink drain, then I’d expect any drain problems to be in the hose itself.)
One additional part of the drain system to check would be the siphon break, which is generally a fixture on the sink upper surface. The dishwasher needs to have an air gap in the drain hose, or it’s possible that a siphon can be set up that would suck all of the water out of the dishwasher when a drain gets started. The air gap prevents that from happening (as it is intended to), but if it gets blocked (since it’s exposed to the air at the sink, after all), then it can interfere with the drain system for the appliance.