The law refers to audio recording. Audio and video with audio recording are unique types of mystery shops. I'm not aware of a law anywhere in the country that make general mystery shopping illegal. As a new shopper, your focus is going to be on non-recorded shops because it is important to get experience in the business first.
Recorded shops can actually be performed in two party consent states. Two party consent means both participants must give permission to be recorded. Some employers get written consent from their employees to be recorded during the course of their job. We should still exercise our due diligence and ask if a target has in fact signed off before performing video or audio shops.
Equal rights for others does not mean fewer rights for you. It's not pie.
"I prefer someone who burns the flag and then wraps themselves up in the Constitution over someone who burns the Constitution and then wraps themselves up in the flag." -Molly Ivins
Never try to teach a pig to sing. It's a waste of your time and it really annoys the pig.