I connected the icemaker to the cold water in the sink area of the kitchen. I changed the single output shutoff valve that was on the cold water, and put a dual output. One side to sink, other to icemaker. I now hear a noticeable "clunk" sound when the upstairs toilet stops filling, and a less noticeable "clunk" when I turn the sink faucet off. Nothing happens for dishwasher, or washing machine. Any ideas?

Did you use copper tubing to connect the icemaker. If so you might move it around behind the friodge and make the sound go away.

I used some flexible plastic hose that said it was for water/icemakers. It came in a spool.

Sounds like you may have a slight case of water hammer. "Water hammer" happens when you abruptly shut off the water. You have at least 40 pounds of pressure pushing the water flow. The weight of the water hitting a 90 degree bend causes the sound that you hear. We put in shock absorbers,(air chambers) to cushion the hammer much like the shocks on your car.
Back in the 60's we were required to to put shock absorbers,(air chambers) on all bath lavatorys and kitchen sinks. Over time water and condensate built up in them and they must be recharged. First turn off the house at the main house shut off valve. Then open hot and cold faucets at the farthest bathroom to prevent air lock.(This is important.) You will find under each fixture little brass or chrome valves. These are called angle stops. With a small pail held under the angle stop to catch the run off look under the handle of the stop and you will see a nut with the stem running through it. This is called the bonnet packing nut. Put your wrench on it and back it off counterclockwise. Now open the stop and remove the stem and washer assembly, The stop will begain to drain. When it has quit draining reassemble the stop and move on to the next one. Do this on each one of your angle stops. There will be six of them in a two bath home. When you are done, close off the faucets you have opened, turn on the water to the house, and give yourself a pat on the back.
You have just recharged your air chambers and saved yourself a hefty service call bill. Hope this helps you out TOM

Thanks for the reply Tom... but I'm a bit confused. I'm not sure what the angle stops are. Can you elaborate some more? My townhouse was built in 85, if that makes a difference and there are 3.5 baths. Thanks again.

Angle stops are the shut off valve in the cabinet. Good luck, Tom

Thanks, the picture is helpful. So if I understand you correctly, I want to undo the nut that's on the side with the handle. Unscrew it all the way and the whole internal assembly will come out, allowing water to drain. Is the right? You want me to do this to all of these, typically 2 for the sink (hot and cold), and then 1 for the toilet. Should I include the kitchen sink as well and any other location with a similar valve... I mean angle stop? Thanks.

You have air chambers on the hot and cold supplies in the kitchen sink and all your bathroom lavatories. Not the toilet. You will have to shut the house down at the house shut off before you begin.

"if I understand you correctly, I want to undo the nut that's on the side with the handle. Unscrew it all the way and the whole internal assembly will come out, allowing water to drain. Is the right?"
Correct.

Good luck, Tom