Continuity mistake: In 1-9 "Road Rayge", Doug and Carrie are sitting watching TV and a song comes on. She tells Doug it is their song, because in junior high he asked her to dance and she said no and gave him the finger. However in this episode we see they first met at a bar and Carrie went home with Richie.
Deliberate mistake: At the beginning of the episode, when Doug and Carrie are in the shower, you see their silhouettes. The first mistake is that for the silhouettes to show like that they have to be evenly backlit which wouldn't make sense in the shower. The second mistake is a little more subtle; you can see the outline where the actor's bathing suits are (inevitably) slightly larger than the bodies. There is also a slight darkening in the areas where the bathing suits cover skin. (both of these things are much easier to see on Carrie than Doug because of her smoother figure and skin tone).