I was in dental school when this came out. I don't know who the dental adviser for the film was but whoever did a great job. This was long before dentists wore gloves for routine fillings and in fact almost nothing except surgery. We were schooled in the proper way to wash and dry our hands; always in front of the patient. Olivier did it exactly the correct way.
He was going to kill Hoffman when he got the information he wanted so why did he care if his hands were clean? It would have been impossible to treat a patient, even if that "treatment" was torture to be followed by murder.
I always thought that was a great touch.