GOVERNOR Chris Patten was not averse to showing off the good condition of his own teeth after a visit to the Prince Philip Dental Hospital yesterday. He emerged, beaming widely, from a tour of the hospital's advanced facilities for maxillofacial surgery, orthodontic treatment and denture-making, to announce that he would be giving the Prince Philip his own toothy custom from now on. ''I have been extremely impressed by what I've seen,'' he said. It was a surprising change of expression from the rather solemn-faced man who began his tour in the Department of Children's Dentistry and Orthodontics. Mr Patten appeared almost overwhelmed by the Space Age-style dental surgery in which up to 37 children can be treated at once. It is unlikely Prince Philip dentists will be called upon to peer into the Governor's mouth in the near future, however. Mr Patten said his last ''oral hygiene treatment'' was only about six months ago.