Botox is used around the mouth for a variety of desired effects. Some professionals use it in small doses in the upper lip to soften superficial vertical lip lines. It can be used sparingly around the mouth for lines / wrinkles there.
Doctors have also administered it into the depressor anguli oris, commonly referred to the DAO muscles. These are muscles found near the jaw line which can help correct an uneven smile or a frown type of look that is ever-present at rest. These are advanced applications that should only be done by an expert provider.