Professor Dixon served as director and principal investigator at the university's Laser Institute, which now carries his name. He has filled administrative appointments as vice president for health sciences, dean of the College of Medicine, executive vice president of the university, and university regent. He has received honors from the University of Utah School of Medicine Alumni, American Society for Laser Medicine and Surgery, Utah Hospital Association, Society of American Gastrointestinal Endoscopic Surgeons and the Utah State Medical Association, and a resolution of commendation from the Utah State Legislature. He also received the Outstanding Professor Award from the School of Medicine student body, was designated an Annual Distinguished Lecturer by the American Society for Lasers in Medicine and Surgery, and a Tutorial Lecturer by the International Society for Laser Surgery.