When Danny's family watches the first episode of the Partridge Family on TV, it opens with the theme song "Come On Get Happy." For the first season of the Partridge Family, the theme song was "When We're Singin'", not "Come On Get Happy."
In the scene where Danny's mother is talking on the phone with his father, the television in the background is showing news footage of President Nixon leaving the White House after resigning from office. In this scene, "The Partridge Family" was still in production. Nixon left office in August 1974. The final episode of "The Partridge Family" aired in March 1974.
On the set, the make-up artist is shown attempting to cover up the blackened right eye Danny Bonaduce received from his father. When Danny is being driven to the beach later that day, it's his left eye that is blackened.
In the opening narrative, Danny explains that each month when the mortgage was due his brother and sister would sit outside while his parents "Re-enacted the fall of Saigon." Saigon fell in 1975, a year after the Partridge Family went off the air so they could not re-enact it since it had not yet occurred.