Legitimate mystery shopping opportunities are out there, but so are plenty of scams. If an opportunity is on the up and up, you won't have to pay an application fee or deposit a check and wire money on to someone else.
You may have heard about people who are “hired” to be mystery shoppers, and told that their first assignment is to evaluate a money transfer service, like Western Union or MoneyGram. The shopper receives a check with instructions to deposit it in a personal bank account, withdraw the amount in cash, and wire it to a third party. The check is a fake.
By law, banks must make the funds from deposited checks available within days, but uncovering a fake check can take weeks. It may seem that the check has cleared and that the money has posted to the account, but when the check turns out to be a fake, the person who deposited the check and wired the money will be responsible for paying back the bank.
It's never a good idea to deposit a check from someone you don’t know and then wire money back.