Revealing mistake: Mrs. Doubtfire sets herself on fire. When she jumps back and starts fighting the flames, it is obviously a stunt double as her face is longer.
Suggested correction: If you look carefully, the face looks pretty much the same, as well as the voice.
The reason the voice was the same is that it was probably an audio dub, which is a voice recording over someone else's voice.
Continuity mistake: In the scene where the social worker is at Mr. Hillard's house and his so-called "sister" (Mrs. Doubtfire) is trying to find a face in the kitchen, one moment the wig is all messed up from being caught on the door. In the next scene, where she is looking in the fridge to find the face, her wig is perfectly in place.
Suggested correction: It was in place because at one point, Daniel even moved his wig and fixed it.
You must be confusing which part of the scene the mistake is talking about. Right before Daniel opens the fridge door, when he has the towel over his face, his wig is messed up, there's even a strand of hair hanging down. When we see from inside the fridge, the wig is perfect without Daniel touching his wig.
Other mistake: When Chris sees Mrs. Doubtfire in the bathroom she is standing up and peeing, in costume. All the scenes where Daniel is putting the costume on shows that the fat suit is a body suit, in one piece, and there's no opening in the front. So he shouldn't have been able to pee without taking off the whole suit.
Suggested correction: Perhaps it can be assumed that he made the necessary alteration (cutting a slit in the bodysuit) before he started to wear it.
Stupidity: Mrs. Doubtfire used the bathroom without first locking the door, enabling Chris (or anyone else) to walk in on her. A man who is dressed as a woman and doesn't want anyone to find out would make sure the bathroom door was closed and LOCKED. (01:07:09)
Suggested correction: Daniel is in his own house, and he may be used to using the bathroom without locking the door. Besides, he probably only thought he was going to be in there for a short time.