Yes, mystery shopping is very legit! You just have to be aware that like with so many things these days, there are people out there with ulterior motives who want to exploit the opportunity and scam people. That's why you see warnings on all the legitimate websites about how they will never send you a check and ask you to deposit it.
It does take time to apply with the numerous companies available, and you don't/won't know if they have shops in your area until after you apply. However, once you get signed up with several companies who do offer shops in your area, you can make a decent side income. It would be very difficult to make a full-time income from mystery shopping, and most articles about it state that. How much you make depends on your efforts, how many shops are in your area, and how hard you want to work! I have a full-time job and mystery shop on the side and average $300-$400 a month. But I do work a lot and will do shops on my way home from work and then on my days off. Also, as you invest time and effort into it and get better at it, then you can be selective and get higher-paying shops and schedulers may even reach out to you at times for assignments. Good luck!