My son will not stop eating his boogers. is this this a sign of mental illness?

Probably not: How old is your son? Depending on his age, this can be a common behavior. If he is otherwise developmentally & behaviorally normal, it is not a sign of mental illness. Of course you should discuss any concerns with your child's pediatrician.

Not unusual: Not unusual for younger children. Try to distract and redirect him instead of correcting him when it happens.