Is there a filter in Kenmore Dishwashers that need rinsing or changing? Our dishwasher seems to be backing up, leaving "silt" on the dishes. I empty the screen on the door, but residue has built up elsewhere.

Water flow problems are what cause streaks, silt or cloudy dishes. The water flow problems can be caused by several things:
1. Clogged spray arm holes (Clean wash arms)
2. Sump inlets that are blocked with debris or plastic (Clean inlets)
Most probable cause.... follows:
3. POOR DRAIN FUNCTION ( a. Inspect all parts of the drain going backward from the sink connection
1) The sink connection is uaually at the side of garbage disposal. Remove the hose from the actual sink connection and clean out the port.
2) The AIR-GAP is the where 75% of the drain restrictions mainfest. Lift off the Air-Gap cover then unscrew the inner cap nut NOTING the installed position of the inner cap because you can only install it ONE WAY. Lift off the cap and remove an debris inside. Use a flashlight and inspect for any debris deep inside the Air Gap,
3) Inspect the Drain hose from the Air Gap to the Dishwasher drain hose connection for any kinks or folds. If you note wither a kink or a fold take a stick over the outside of the hose like you were putting on a splint.
4) Remove the drain hose from the dishwasher connection and inspect for debris. Clean as necessary. Just note there is power under the dishwasher that can reach out and grab you so make sure the power is off before working under the dishwasher.

Reassemble everything power it up, use the Jet Dry basket type even if you have a rinse dispensor. Please let me know how the dishes turn out.

Thanks for choosing FixYa,
Kelly -->-->

The problem is most likely that there is still water residue at the bottom of your machine. If the machine is not fully drained it picks up some of the residue and sprays that onto the dishes during the final rinse, leaving an unhealthy and unsightly film on everything.
Remove the bottom strainers plates and make sure that the outlet pipe is not kinked, that there is nothing obstructing the pipe or the pump or selector valve. If possible back flush through the outlet pipe and try draining the machine once more before using it again.