A Korean mom I know said recently that there might be an issue on the Korean side, as military service is mandatory for Korean males (maybe you are female and it would be a non issue?). Wikipedia is clearly not the best legal source, but it indicates there that you would need to renounce citizenship before age 18 to avoid the service requirement there. You can find that info elsewhere also.
In other words, if you ever wanted to visit Korea again (like for example if you are in the American military and want to serve a tour in Korea...) without having renounced, it could be an issue on their end. This source indicates that you have to have been registered in the "Korean Family Registrar" though for it to be an issue.