The shark that Michael kills to protect Sawyer is tattooed with the Dharma logo on the tail.
During a flashback to a younger Walt leaving for Europe, Michael gives him a stuffed polar bear.
In the hatch, when Desmond recognizes Jack from the stadium stairs in L.A., he leaves and says "See you in another life, yeah?" like he did in LA.
The Dharma orientation was on the top shelf behind Turn of the Screw, a novel by Henry James. This story has been turned into a few different film versions that allude to a woman caring for kids who are actually ghosts, or whose parents are ghosts.
In the orientation film, the VO compares the Dharma Initiative to that of the work of B.F. Skinner. Skinner created the Operant Chamber, a controlled environment to gauge the responses of its inhabitants; in his case, rats. Here’s a brief synopsis of the experiment.
The film goes on to discuss the initiative, stating that they had intended to study psychology, meteorology, parapsychology, zoology (showed two polar bears in this part of the film) electromagnetism, etc. Alvar Honso financially backed it. People are in stations for 540 days. Electromagnetic fluctuations are being studied from the Swan chamber where Desmond is.
Edited down from something I found on Lostpedia:
According to the 1975 orientation film in the Sri Lanka Video, the Valenzetti Equation "predicts the exact number of years and months until humanity extinguishes itself." During the video, Alvar Hanso also states that the radio transmitter on the Island, will "broadcast the core numerical values of the Valenzetti Equation;" 4, 8, 15, 16, 23 and 42.
Alvar Hanso also states in the video that the purpose of the Dharma Initiative is to change the numerical values of any one of the core factors in the equation in order to give humanity a chance to survive by changing doomsday. However, Thomas Mittelwerk reveals that as of 2006, they have failed to change the values through manipulating the environment, as the equation continues to arrive at the same six numbers. It is unknown how or if the most recent calculation of the equation is automatically reflected in the radio transmissions.
Rachel Blake also learned that the Hanso Foundation was forcing savants at the Vik Institute in Iceland to run the equation over and over. Somehow, five hieroglyphic symbols were involved in the calculations (Armand Zander described them as "representative"), the same hieroglyphs seen on the countdown timer in the Swan station.
Jack asks Desmond if he ever wonders if it's all a mind game.
Desmond is reading a book called The Third Policeman.
This is also the time where I must say, I cannot STAND Anna Lucia's character. That bossy, effin loud-mouthed bitch deserved to get killed off. Actually, I read that the actress playing her got two DUIs on Hawaii and was booted. Neener neener.
In the episode "Fire + Water," Charlie was hallucinating. One of the things he saw was Claire and his mother as angels, as well as Hurley in some sort of holy getup.
Henry Gale is the name Ben Linus gave when Sahid found him in the hanging trap. The real Henry Gale is connected to Widmore and to the chicken place where Hurley worked.
Sawyer is always reading, and we see him reading a book by Walker Percy, a Southern author who was fascinated with signs and existential thinking.
He’s also reading Judy Blume’s “Are You There God? It’s Me, Margaret.”
Claire has another flashback to when Ethan was examining her, then showed her a nursery for her and the baby. The mobile over the crib is a bunch of Oceanic planes. The song that plays from it is “Catch a Falling Star,” which is what Claire asked the woman who was going to adopt her baby to sing to the child.
Ethan goes out to talk to a man, clean-shaven with white hair. He looks familiar, and then later when Claire, Rousseau and Kate break into the Dharma station where Claire was held, Kate finds theatrical glue and a beard. The clean-shaven man was the dirty-looking “other” who confronted Jack, Locke and Sawyer when they were trying to get Michael back.
What is UP with Sun’s hair? When she got on the island it was short. 60 days in, it’s all the way down her back.
Episode 18, Hurley reencounters his imaginary friend, Dave. He tells Hurley that the island is all in his head. Hmm. I really hope Lost doesn’t end up being all a dream… When Dave goes to jump off the cliff, he says “See you in another life, Hurley.” Just like Desmond says to Jack. Libby finds Hurley on the edge of the cliff, makes him realize that none of this is in his head, and then we see Hurley in the mental hospital in a flashback again. The camera pans to a woman being given her meds, and it’s Libby.
In the episode “S.O.S.” Rose and Locke are talking on the beach. Locke is frustrated about his leg, claiming that Jack said it’ll take four weeks to heal. And Rose says “Honey, you and I know it’s not going to take that long.” Then Rose is shown in Australia with a healer, who tells her that “this is not the right place.” In reality, the island has healed her.
When Ekko goes to investigate the “miracle” of a drowned girl coming back to life, her father confronts him at the door. It is the same man who was the psychic that kept trying to warn Claire of danger.
When Locke and Ekko find The Pearl Station, we learn that it’s an observation station, designed to observe other stations and the inhabitants’ actions, in a psychological experiment. Ekko says “We are being tested. We do it because we believe we are meant to.”
During a flashback to when the Others took Michael to their camp, a woman named Mrs. Clue asked him some questions. One of the thing she asked him was “Has Walt ever shown up in a place he wasn’t supposed to be?”
I love Sawyer. Really. Truly.
The statement that continuously keeps coming up is island inhabitants saying “do not tell me what I can and can’t do.”
Also, in a Desmond flashback, he doesn’t have any U.S. currency to pay for a coffee. We see a woman paying for it and it’s Libby. After sitting down for coffee, Libby confesses that her husband has died, and she ends up giving Desmond his boat so that he can sail around the world to win Penny’s love. Interesting that this boat is the one the survivors see at Libby’s funeral.
Desmond flashes back to crashing on the island and being picked up by men in yellow suits, then put into one of the hatches. The man who questions him is Kelvin Inman, the American military guy from Iraq who questioned Sahid. Otherwise known as The Kergen from Highlander. He’s the one who drew the map on the walls of the hatch.
The logs that were sent in pneumatic tubes are all found in a giant heap on the island. Another sign that the people in the hatches are part of an experiment.
When the party going to get Walt realize they are nowhere near the beach, the whispering voices start up. One of the first things said is “Elizabeth,” which is Libby’s name.
At the very end of Season 2, two men out in the Pacific listening post are playing chess. They see that there is an electromagnetic anomaly, and then call Penny.
