I've had a few customers with water pressure that fluctuates in the shower, just one side. Sometimes you have a pressure drop off if someone is using other plumbing that drops the flow for a moment, maybe a toilet being flushed, a washer cycling on, or someone at the kitchen sink.
Sometimes it gets stranger though. Sometimes the problem faucet is the only fixture being used, and it has a maddening little quirk about it. Pressure may flutter or fluctuate for no good reason. One time on Mercer Island I found a round plastic ball in the cold water side. I removed the shower valve and there it was. It was most likely a ball from the heat trap nipples of the water heater that had flowed downstream.
This week, a customer in Bellevue had the problem on the hot side. Plenty of crud had been accumulating in the aerators of the faucets, and the water heater was running out of heated water sooner and sooner. The eight year old Water heater was behind the tub in question, so we pulled and replaced the water heater, and installed a new Moen Posi-Temp tub shower valve with new trim. The old Moen valve, when removed had junk in the hot side pipe. The picture below shows the broken bits from the old dip tube.