Problem: My Kenmore Elite model 417.4110 rinse and spin cycle ends but the water keeps pouring.

Your water level switch is the problem. Not necessarily the switch, but possibly and more likely the tube going to it. It has a tube that attaches at the bottom of the tub and to the diaphragm on the switch. Pressure from the water level rising turns off the switch to indicate that the tub is full. You need to make sure it's attached tightly at both ends. Many times you will need to cut off a little bit on each end and dip each end in hot water to soften the plastic and reattach the hose. Sometimes the hose gets a hole in it (rare), but most of the time it comes loose from vibration or not being attached well at the factory or from being moved. If the hose is fine you need to check the switch by placing the leads of an ohm meter set to lowest scale on the terminals on back (turn off power first by unplugging). There is a common (power in), a normally open, and a normally closed terminal. You blow on hose as you check it with the meter with one end of hose on switch. The normally closed part of switch will open and the normally open part will close. It's very simple. Look at these: https://dl.dropboxusercontent.com/u/8010163/Kenmore_Elite_Calypso%20Washing_Machine.pdf
https://dl.dropboxusercontent.com/u/8010163/Kenmore_Washer_Elite.pdf
https://dl.dropboxusercontent.com/u/8010163/Understanding%20automatic%20washer.pdf
https://dl.dropboxusercontent.com/u/8010163/How%20to%20use%20Test%20Equipment%20Service%20Manu al.pdf