I was wondering where I could download a service manual for my Kenmore dishwasher... Mod.#587.16072201 Thanks,

I think this is what your looking for but I'm not sure...
User Manual: Kenmore 587.16072200 Dishwasher (http://kitchen.manualsonline.com/manuals/mfg/kenmore/58716072200.html)

It's off by one digit in the model # but maybe you can poke around the site a bit and find what your looking for.

In case you need the user manual, please see the previous post. However, if you want learn how to diagnose and replace faulty parts, you will need to consult the service manual (if you don't want buying new dishwasher and paying someone to repair it)
It depends on whether you are really a DIY type and how good you are with appliance repair and electricity. The service manual for this washer can be found at Kenmore Dishwasher Service Manual (http://www.allrepairmanuals.com/kenmore-dishwasher.htm)Make sure to have the model number handy (you can find it behind the door).
Most problems with d/w can be due to food particles getting into the system. The service manual shows how to take them apart for cleaning.