Caesar is panicking at the beginning of the episode because Luke is leaving for 10 days and Caesar states that he's never been away for that long. Luke, however, spent 7 weeks away helping Liz and TJ at the Renaissance fair when they were both injured. He also went on a seven-country cruise for a summer with his then-fiancee Nicole during Season 3.
In Welcome to the Dollhouse (2005), Taylor Doose renamed all of the town's streets to historical Stars Hollow street names (i.e. the Dragonfly Inn's street name was changed from 3rd Street to Sores and Boils Alley), but Richard, Lorelai's father, says he and Emily parked on Peach Street, a post-historical street name.
Jess sends Rory's invitation to Logan's apartment, yet when she goes to see him and he learns she is still dating Logan, he is surprised.
The boy on the bus who knows "300 digits of pi" recites "14201995611" which is nowhere in the first 300 digits of pi. "4201995611" is digits 701-710, but is preceded by a 5 not a 1.
When Luke is passing out food to the kids and asks who can't have dairy, he sets the food down for the kid and says, "No mayo." Mayonnaise doesn't have dairy.
When Mrs. Kim brings her wedding dress to Lorelai for alterations she tells her that she was married to Mr. Kim 28 years ago. When Mrs. Kim has her sex talk with Lane in the next episode, I Get a Sidekick Out of You (2006), she remarks that maybe she will be lucky like Mrs. Kim was and only have to do "it" once. This would make Lane 27, but she is only 22.