Originally, Klaus was going to be French, and named François. When Dee Bradley Baker auditioned, he told the producers that his French wasn't very good, and that he would read the lines in German instead, they liked his performance so much, they retooled him so he was German instead.
Steve's original design was much geekier and gawky, and he was voiced by Ricky Blitt. Halfway through production, his voice actor changed to Scott Grimes and his design was made to be more attractive, so he would be less comparable to Neil Goldman, from Family Guy (1999). This design is a caricature of one of the series creators, Mike Barker.
Hayley says in American Dad!: Stan Knows Best (2005) that she is eighteen years old. Based on this information, we can assume that she was born in either 1986 or 1987 (depending on her month of birth).
The uniformed officer in the Underdog Productions logo at the end says something different in every episode. (Not unique, just out of a small assortment.) In the season seven finale, he was given a speaking role as Steve's imaginary friend "Pedro".
The final frame of the introduction was changed for seasons beyond the first. At the end of the credits in the first season, all that could be seen was a big "American Dad!" logo in front of the American Flag. In all subsequent scenes, this logo was shrunk to fit the names to the series creators on the same screen.
In "Meter Made", Francine asks her adopted sister Gwen "how are you enjoying being three years younger than me". Later, in "Now and Gwen", Gwen is a senior in high school while Francine is a freshman, making her roughly three years older.
In the season three episode "Camp Refoogee" Stan flies to Africa and turns a refugee camp into a summer camp. However, in the season seven episode "Ricky Spanish", a sponsored child from Africa, named Tungee, comes to live with the Smiths. Stan asks, "Does this mean Africa's real?"