The Dharma logo in the show is encircled by symbols known as "Trigrams". There are eight Trigrams altogether, each representing an aspect of life. One of the Trigrams can be seen on the tower of the submarine as Juliet is standing on it. This Trigram represents the 'front door', the beginning or your life path, and career.
The song playing on the radio when Juliet arrives to meet Alpert in the first flashback is "Downtown" by Petula Clark; the same song she was listening to the morning of the day the plane crashed on the island.