Shinespike, there are two ways to handle expenses that are reimbursed -
1) do not include them on your Schedule C at all
2) include them as income on Schedule C and then deduct them as business expenses on Schedule C
Reimbursed required expenses are not taxable to you and neither of the approaches above will result in taxes due to reimbursements.
But here are some thoughts:
You want your business to look like a 'business' rather than a 'hobby'. If mystery shopping is a hobby, you get no deductions from your mileage, equipment or other normal business expenses. Approach 2) shows a higher gross 'income' and after appropriate deductions has no more taxable income than approach 1) but makes your endeavor look more like a 'business' than a 'hobby'.
Sometimes you may take some 'fee only' shops that require a purchase. Reasonable amounts for those purchases should be deducted from your Schedule C as 'unreimbursed expenses', which of course then highlights that there may have been some 'reimbursed expenses' to discuss.
Not all companies you work with get competent tax advice (or perhaps they just don't understand what their tax advisor is saying) and 1099s sometimes include reimbursements as income to you. IRS has been told those companies paid you X, while what they paid you was X - reimbursements when it comes to taxes. If you are not claiming reimbursements in the Gross Income of Schedule C, you quickly get into a conundrum of trying to figure out what to do with the excessive claims of the 1099.
Finally, should IRS decide to look at your cash receipts (Paypal, direct deposits, checks deposited, etc.) you will have to reconstruct why you 'received more than you earned'.
So as far as I can see there is zero reason to go with approach 1) even though it is a technically correct answer. With approach 2), every penny received is claimed in Gross Income, whether it was fees, bonuses, mileage, reimbursement or whatever. I make sure that Paypal sends money to the same account that direct deposits go to and that other payments get deposited to. Any IRS inquiry will be easy to match up the Paypal statements with the money movement and the rest of the deposits are all there with vendor. When 1099s come in I don't worry about their accuracy as long as they are in the ballpark.
Because you have another job, make sure you are aware of the differences between commute mileage and business mileage because pulling through McDonalds to do a shop on your usual route to your job is done on 'commute' mileage rather than 'business' and commute miles are not deductible.