Staying safe and health at the spa is not much of a worry unless you're going to get some of the more aggressive chemical skin peels and laser hair removal.
An aesthetician is only licensed to use light to light-medium peels that work on the outer layer of skin - the epidermis. If she works under the supervision of a medical doctor, in a "medi-spa," she can administer more aggressive peels that penetrate further. You should undertake these with caution.
Laser hair removal is another area that requires a highly experienced, skilled practitioner. Factor like skin color and what medications you're taking affects how you respond to the treatment. Be completely honest about whether you're on anti-depressants, for instance, or burns could result.
After getting a massage, sit up slowly, and make sure you aren't dizzy before you step off the table.

