What kind of skin problems cause arise due to overdose of anesthesia?

Probably none. : None that I have ever heard of or encountered. Would need more specific detail.

Allergy: "skin problem" like rash may be an allergy. Overdose in anesthesia would lead to complete loss of braiwaves, which should be reversible if blood pressure and breathing is supported during the surgery.

Usually none: A patient can have skin reactions to any medications that they have been given. However, there is not usually a reaction to anesthetic agents per say. There have been reports that exposure to anesthesia can cause alopecia, or hairless, though the mechanism is unclear. I hope that this helps.

?: Is there something specific you are concerned about? I can't think of any ways that an anesthetic overdose would affect the skin specifically.