What health conditions threaten a successful recovery after scar revision & mole removal?

Immunosuppression. In addition to diabetics, patients who are immunocompromised (ie: hiv, organ transplants, chemotherapy for cancer, etc.) also have slower healing and increased risk of infection.
Diabetes, tobacco. Any health conditions that prevent proper wound healing. This includes diabetes, peripheral vascular disease or any conditions that narrow the small vessels going to the surface of the skin, in particular tobacco use (smoking). If you do smoke, quit at least 3 weeks before the procedure. Also avoid blood thinners like Aspirin and Ibuprofen as they can increase risk of bleeding from the wound.
Diabetes. Diabetics may heal slower. Tension on the wound and excessive movement may result in a worse scar. Discuss after care with the doctor who performed the procedure.