I cleaned my shower head by wrapping it overnight in a plastic bag filled with vinegar. The next morning I took the bag off and scrubbed it with a toothbrush.
Here is the shower head operating before cleaning.
Here is the vinegar I used.
Here is the shower head with the bag of vinegar wrapped around it.
Shower head had a little buildup, and I was cleaning the kitchen faucet aerator anyway, so why not use the same vinegar bag? I wiped down the shower head and individual nozzles and soaked it in vinegar for a few hours. Much cleaner, and the nozzles run smoother now.