All income is taxable whether it is paid in cash, deposited in your account or mailed by check and regardless of whether it is reported on a 1099 form. The difference is that if one company or individual pays you more than $599 in a year, they are obligated to report that payment to the IRS -- so if you don't report it, you are likely to get caught.
BUT, that doesn't mean you have to pay taxes on the full amount. If you do mystery shopping seriously and run it like a business (i.e., you actually make some money doing it and are organized), then you get to deduct your costs of doing the work. These would include things like auto mileage, cost of making copies, even cost of equipment that you have to buy (e.g., digital camera, computer, scanner -- if these are used primarily for your business.) All of this belongs on Schedule C of your tax return. You only pay taxes on the net profits.