Johnny Galecki had met Judd Hirsch at the James Burrows tribute show long before this episode, and had personally asked him to play Leonard's father. Galecki really wanted Hirsch since he had already patterned Leonard after Hirsch' character Alex Reiger from Taxi (1978), who was also one of the more normal people in a group of crazies.
The pink photo frame with the picture of Penny's old car that she gave to Leonard in The Expedition Approximation (2014) can be seen in Leonard's bedroom.
Judd Hirsch, who plays the father of physicist, Leonard Hofstadter, has a degree in physics. He earned it from the City College of New York, circa 1956.
After this episode Penny will have had three wedding ceremonies: two with Leonard (the first one occurring in The Matrimonial Momentum (2015)), and one with her ex-boyfriend Zach (Brian Thomas Smith) whilst intoxicated in Las Vegas, as revealed in The Thanksgiving Decoupling (2013). When Penny tells Leonard "I never thought my second marriage would be to you", she is technically not incorrect depending on law: her marriage with Zach was officially annulled due to 'want of understanding' (rather than ended through a mutually agreed divorce). In most cases, a marriage that is annulled because it is unlawful is also retroactively voided, meaning that it is considered to never have taken place. This would make her second wedding to Leonard also her overall second wedding, not her third. However, it could of course be argued that it wouldn't constitute a "second marriage" either, since it is not a legal wedding ceremony.