The words Dogen muttered as he left Hugo in the temple hallway were "You're lucky I'm supposed to be protecting you here. Otherwise I would've chopped your head off", in Japanese.
Jack's son, David, is reading "Alice in Wonderland", which is a common theme in the series. Episode five of season one is called White Rabbit (2004) and one of the Dharma stations was called the Looking Glass - all Alice in Wonderland related. Also, in Something Nice Back Home (2008) the book Jack is reading to a sleeping Aaron as a bedtime story is "Alice's Adventures in Wonderland".
Hugo wanted to position the mirrors to 108 degrees. That's the sum of all hatch's numbers: 4+8+15+16+23+42=108.
The sheet music in David Shephard's room, that he was also playing in his audition, was for Chopin's "Fantaisie-Impromptu", which was the piece young Daniel Faraday was playing in The Variable (2009).
A poster on the wall of David's room advertises the band Meat Coat, which is the band Charlie tells his brother they have a chance to open for in LA in The Moth (2004).