There have been no cases, to-date, of which I am aware of permanent nerve weakness induced by Ultherapy.
Nerve weakness could occur from heating a nerve if the energy delivered is in the area of the nerve. The nerve may then hibernate and take a few weeks to recover. Meanwhile, muscle weakness could cause a failure of the corner of the mouth to lower when the whole mouth opens, making it look like the other side is drooping. This is from temporary irritation of the marginal mandibular nerve and so the area in which the nerve becomes less deep near the corner of the mouth is not treated with the deep-reaching transducers, but doctors have been able to use, off-label, the new 1.5mm superficial transducer with a greater treatment area while they avoid the 4.5mm. deep transducer in the avoidance zones.
The information provided in Dr. Shelton's answer is for educational purposes only and is not intended to constitute medical advice. The information provided should not be relied upon as a substitute for consultations with a qualified health professional who may be familiar with your individual medical needs. If you are experiencing a medical emergency proceed to your nearest emergency room.