Continuity mistake: It is known that Dorothy married Stan because she was pregnant and they were married for 38 years. However, we know Michael is not 38 (in a couple of episodes they state his age as either in his 20's or 30) and in the 2 episodes her daughter is in, she doesn't look to be anywhere near 38 either.
Continuity mistake: In one episode, Rose talks about being valedictorian of her high school class in St. Olaf. In another episode, Rose goes to night school (where Dorothy is her teacher) in order to get her GED because she never graduated from high school. While talking to rose about the class Dorothy states the class is for people who didn't get a diploma. Additionally, in the episode "Whose face is this, anyway" Rose mentions that she was in a sorority called the "Alpha Yams"; when the girls look at her strangely, Rose states "It was an agricultural college." She could not have gone to college without a high school diploma.
Continuity mistake: In the episode when Dorothy is trying out for Jeopardy, she is sitting on the couch studying, When Sophia sits down to talk to her Dorothy is looking at a page with just words, It cuts to Sophia and then to Dorothy and the page now has pictures on it. You can still see the corner of the book when the frame is on Sophia and you can see that Dorothy did not turn the page.