I set the side switch to "lock rotation" in "settings". and when I flipped the side switch back & forth -the screen stayed in the same position and continued to show the "rotation lock" icon in the status bar, no matter which position the side switch was in.
while the settings for the side switch were in "lock rotation", I was able to mute and un-mute sounds, but using the side switch did not allow me to lock or unlock rotation - once it is set to "lock rotation" in the settings for the side switch, the side switch does not allow screen rotation to be unlocked (same goes for when the side switch is set to "mute" in settings - using the side switch will not allow sounds to be muted or un-muted when "Mute" is clicked for side switch in settings.)
also, I read in the iPad troubleshooting section that turning off the iPad completely by using the power switch at the top of the iPad, then waiting a bit and turning it back on using the power switch may reset things; however, when I did this while the side switch settings were set to "lock rotation," instead of getting an intermittent bell with the line through it (alternating with the bell with no line), I got the rotation lock icon intermittently (alternating with the rotation unlock icon) for a few iterations when the iPad restarted.
sooooo.....I'm about ready to give up and go see a genius 😉 lol