Lauren Graham and Alexis Bledel don't share any scenes in this episode
The one armed surfer and the shark Lorelai mentions is a reference to Bethany Hamilton. She was surfing when a shark bit her arm off.
The hat Lorelai is wearing that Luke comments on is a Bon Jovi hat. "Livin' On A Prayer" is a Bon Jovi song.
Both Lorelai and Rory cry for failing in their lives.