Lower eyelid cosmetic surgery continues to be the area where surgeons can create significant complications despite performing a standard surgery. A big reason for this is that for the most part, the paradigm for lower eyelid surgery is fundamentally flawed. The general plastic surgery literature oversimplifies the anatomic approach to the lower eyelid and the key papers in my opinion incorrectly present the anatomy. Plastic surgeons continue to use the trancutaneous lower eyelid incision to approach lower eyelid fat. This is done through a cut just under the lower eyelid lashes and the muscle just under the skin. According to key papers in the plastic surgery literature, this leads the surgeon into a potential space and the dissection can be done without damaging the nerves that supply the muscle that supports the lower eyelid. This description is not actually based on observation but rather just a theory. Many other papers do not support this description. This is consistent with clinical experience with many injuries and lower malpositions developing after this type of lower eyelid surgery. The problem is often compounded because the surgeon attempts to correct an unrecognized motor nerve injury by tightening the lower eyelid (canthoplasty). This often further compromises the lower eyelid position. I know because I make a living fixing this type of situation.
The answer is to avoid having a surgery that violated the muscle plane. It is important to have an explicit conversation with your potential surgeon regarding what approach they are planning. If they are not prepared to have this detailed a conversation with you about your eyelid surgery, you should consider seeing a different surgeon.
Other complications, sure there are many other potential complications but they are less frequent. The important thing is to really do your homework and understand what is being proposed to you. If you can understand the anatomy that I have described you will be ahead of many plastic surgeons offering lower eyelid and transcutaneous mid face surgery out there.