Other mistake: When playing poker, Stef says she has all hearts which is a flush. However if you look at the cards she puts on the table, there is a 6 of diamonds and 3 of clubs. Therefore, not a flush. Everyone at the table, (Lou, Mr. Prezants, Deacon, Spencer and Doug) all agree it's a flush.
Continuity mistake: In the episode where Priority Plus is mentioned, after the Priority Plus driver has got Doug out of the drive through, he gives Doug a lift in his truck. In some shots there is a window on the side of the street. In the window there is no Priority Plus truck visible.
Add timeA Demon
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).
Audio problem: When Doug enters the kitchen wearing his leather jacket and tells Carrie he just got in from riding the bike, you can see the bike parked just outside the kitchen window in the backyard. If that was true it would have been heard from inside the kitchen, as motorcycles are quite loud.