When Miles takes Daniel to the construction site of the "hatch", Daniel is wearing a black jumpsuit and when he comes back up the suit is light gray.
The footage of the sunk airplane is by far too bright; the lights mounted on the ROV's filming objects that big in such deep waters can only illuminate comparably small areas.
1977 Dharma personnel use Sig Sauer P226 pistols, a weapon which was not designed until the early 1980s.
When the young Daniel Faraday is playing the piano, the actor is only pretending to play.