He has no written authority or directive that allows him to enforce Army standards.
That however does not mean that you should just blow them off. If you are doing something wrong I would encourage you to take the on the spot correction as one professional to another. If you choose to become aggravated with the retired Soldier he may know your chain of command or at minimum report the incident which then elevates the issue to another level of which you most likely do not want that kind of attention. If you act inappropriately and your behavior does not cast a positive light on the military then yes your chain of command could choose to act on the information and implement corrective training or worse.
Best policy thank the retiree for their correction and service and disengage. There is no trophy to be won in a pissing contest with a retiree. Most retirees are just trying to help in the rare cases where one of then still thinks they are on active duty…kill them with kindness, it goes a long way in deflating their argumentative behavior. Bottom-line if you are wrong make the correction in a positive and upbeat manner.