When Lorelai and Rory emerge from the bushes, Lorelai says "See, three minutes faster," implying she found a shortcut from their house to Sookie's house. In reality, the outside of Sookie's house is the backside of Lorelai's house and the writer is making a nod here.
The song "Those Lazy-Hazy-Crazy Days of Summer", which is sung by the barbershop quartet (in the gazebo) throughout this episode (and which inspired the episode's title), sounds like some old-fashioned song from the turn-of-the-century, when barbershop quartets were popular. But in reality, the song wasn't released until 1963, as a record by singer Nat King Cole.
During Lorelei's dream she said she decided to change the name of the twins to Leopold and Loeb, in season 1, Star crossed lovers and other strangers, Chase said the name of his dobermans were Leopold and Loeb.
When asked how she has enjoyed the nations Capital, Rory says she got to see Archie Bunker's chair. Recurring character, Babette is played by Sally Struthers who also played Gloria, Archie Bunkers daughter on All In The Family.