How can I troubleshoot the cause of problems in a washing machine?

Our machine sticks on the washing cycle in about 3 places. After calling the repair man, I noticed that he went through a series of questions, eliminating causes and highlighting other clues.
ie. I asked if it was the pump; and he told me to run it through the rinse-spin cycle. If it pumps the water out fine, the problem is not with the pump.
I would be very interested to see a list of these conciderations that can track down the problem. In heinsight, the pump thing is obvious; but I would not have thought of it myself.
(The machine is a whirlpool).