Emily tells Lorelai the auction was on Tuesday. But before Rory and Lorelai go for Friday night dinner, Lorelai is on the phone with the people who held the auction. She tells them she went to their auction yesterday. But "yesterday" would have been Thursday, not Tuesday.
When showing Lorelai how his sprinkler spigot works, Dwight demonstrates that turning it right (clockwise) turns it on and left (anti-clockwise) turns it off. Later, Rory turns the spigot anti-clockwise and successfully turns the sprinklers on.
When Lorelai and Rory go inside Dwight's house and are talking about the tiki bar, Rory says Lorelai likes Pina Coladas to which she replies "and getting lost in the rain." The correct lyrics to the song are "getting caught in the rain".
In S3 E5, Lorelei is talking to Peyton on the phone when he is asking her out, she repeats to him that he just got back from Maui but you can see that she clearly did not say Maui.
When Lorelai and Rory are leaving in the morning to water Dwight's lawn, a boom mic is briefly visible in front of Rory's room.
At the auction, Emily is referred to as "The Cobra" because she squeezes people until she gets what she wants. Cobras are not constrictors, they are vipers. Python or Boa Constrictor would have been correct.