A mystery shopper job is likely to be a scam if it requires you to pay any of your own money to gain the job or perform the job requirements. An application fee is a good indicator of a scam, as is the need to deposit or wire money to an account.
Fees for applications are usually justified by scammers as a cost requirement for guaranteed work or for certification in order to increase your chances of obtaining a job. Lists of companies looking for mystery shoppers are widely available online, and certification is not necessary to secure a position.
Another scam used by mystery shopper advertisers involves having the shopper check a money transfer service as an assignment. The supposed shopper is sent a check and instructed to deposit it into a bank account. When funds are available, the shopper wires them back to the sender. The check is usually fake, and the funds used are the responsibility of the scammed shopper. There are several versions of this mystery shopper scam, but they all revolve around wiring money to a third party. A portion of the funds are often paid to the shopper as incentive to complete the transaction.