According to one biography, Robin Williams decided to test out the believability of his Mrs. Doubtfire character during filming by going as Mrs. Doubtfire into an adult bookstore and making a purchase. He was able to do so without being recognized.
Chris Columbus was amazed how far Robin Williams took his performance. First, he played each scene as scripted two to three times, and then was allowed to improvise, or "playing" as Williams called it. Columbus allowed Williams a lot of improvisation, because that was where the film's funniest material came from; in fact, Columbus called it magical at times.
During the scene when Mrs. Sellner comes to inspect Daniel's apartment and Daniel/Mrs. Doubtfire is serving her tea, the icing on his/her face is melting off. This was not intentional. The heat from the set lights melted the icing on his face and Robin Williams improvised the bulk of that scene.
Chris Columbus would use two or three cameras at a time when shooting Robin Williams' scenes, uncertain of what the famously improvisational actor would come up with. Columbus viewed shooting these scenes as if he were making a documentary.
Robin Williams did interviews as Mrs. Doubtfire to promote the film, and sometimes played the interviewer too.