No, you don't.

There are a whole lot of scams out there that try to get people to pay money to learn how to become a mystery shopper, but just like any other job all you have to do is find someone who is hiring. Try contacting the corporate offices of several large retailers to see if they can offer you any further advice.

Check my source below; there, you can check the links at the bottom of the page to find online discussion groups dedicated to secret shopper jobs as well as a couple of organizations that may offer such a job.
References :
http://en.wikipedia.org/wiki/Mystery_shopper#Fraud

No you shouldnt have to pay money to get a job (whatever type of job it is) Its just a scam if you have to pay. Im sure there are some companys that employ mystery shoppers but I dont know of any. Also Im assuming that those companies wouldnt have to be putting ads anywhere to find employees.
References :

My mother in law is a mystery shopper, and I was for a little while.
Some companies make you pay a fee while others don't. You always have to pay out of pocket for the things that they make you purchase but they do reimburse you for it, plus a small stipend, later on. Also, mystery shopping isn't a "big bucks" job, the average pay for a "shop" is between $5-12 and generally the most they will reimburse is less than $10. The more you have to do for a shop the more you generally get paid but most times all you have to do is walk into a store, interact with an associate, ask about a particular item and that's it.
Try these companies… it's free to sign up on them (or it was when I joined):

http://www.servicesleuth.com/
http://hellomirror.com/index.norm.php

Good Luck!
References :

Here are a few FREE Mystery shopping sites you can sign up for!

http://www.sparksresearch.net/apply

http://www.mysteryshopperservices.com

http://www.consumerconnection.net

http://www.mystshopsol.com

http://www.beyondmarketinggroup.com

http://www.baidata.com

Happy Shopping!!!!!
References :