While you are waiting for a response, read through the mystery shopper FAQ for your particular company as they may have the answer listed there.
If the problem is urgent, you may need to attempt an actual phone call. This can be if you are onsite for a mystery shop job when it arises. The goal here is to be as discrete as possible. It may be best to step away from the establishment or return to your car.
Bonus tip: Employees have to go to the bathroom too. You do not want to risk being discovered by calling the mystery shopping company while hiding out near the toilet.
The smartest thing to do is prepare in advance for issues or shop problems. Many mystery shopping companies have a frequently asked question or FAQ section on their website. This area would, more than likely, cover many issues that could arrive for a new or seasoned shopper. The FAQ area could also lend suggestions on how to best address the issues.
Another area to check would be the actual shop assignment section. The shop guidelines will be posted here. Read them ahead of time. Read them right before the shop. This will save you lots of trouble later.
Again, if after all of the above, you still have questions, this is where you can reach out and e-mail the support staff for guidance.