Revealing mistake: When the Hillards are at the pool, we see Stu, with his hairy chest, on the diving board. When the shot zooms out, we see a guy with no hair on his chest, who is obviously the stunt double.
Continuity mistake: In the scene in the kitchen while Daniel is looking for a face, his robe is not closed completely at the top, but as soon as Mrs. Stelner enters, the robe is done all the way up and quite tightly. After the face cream in the coffee, Mrs. Doubtfire leaves but quickly sticks her head back in the kitchen and her robe is again loose at the top.
Continuity mistake: Daniel (disguised as Mrs Doubtfire) is cooking and knocks the cap of the pepperpot into the frying pan. In the following shot, Daniel hasn't removed the cap, but it's not there any more.