Equinox
In the Lamppost station there is a photograph of the island from 1954. Specifically, Sept. 23rd, 1954. This was the date of the late-year equinox that year. In 2004, the same equinox landed on Sept. 22... the date flight 815 crashed on the island. Some sources have Naomi finding the island on the late-year solstice of 2004. Is all of this coincidence? I doubt it.
Now, Henry Gale is claimed by Ben (when he was pretending to BE Henry) to have arrived... well, not on an equinox or a solstice. And we don't know about when Desmond arrived. But these dates we do know are either Easter eggs or they hold some significance.
Claire claimed to know a few things about astrology. If she knew enough, she ought to be able to recognize certain constellations in the night sky and have some familiarity regarding where they should be relative to time of year and location of the observer. If the island jumps around in space and time, a star-gazer would notice. She would also have a sense of when the equinoxes and solstices are, as they typically mark the edges of zodiac signs. When Claire first mentioned knowing something about astrology, that seemed important, but it hasn't come up again since (waaaay back in season 1). Might it yet serve as an important clue?
Not coincidences, but not helpful either...
...at least not the way the material has been presented anyway. Carl mentioned a perticular constellation when camping in the jungle with Sawyer (the night Claire disappeared?).
The problem is the average watcher doesn't have that in depth knowledge of astronomy so the writers have to literally hold our hand and walk us through it, which as you've commented, seem to have left it behind waaaay back in S1.
But when I found out Lost was partially based on the PC game MYST, I replayed the game and found the constellations were used as clues to solving some other puzzle that when solved allowed you access to another world - via a linking book (the Book of Law alluded to by Eko?). And wasn't the Book of Law one of the items Alpert showed to young Locke as part of Locke's test? But I digress.
In the case of Lost, I believe the Focoult Pendulum Eloise Hawking is weilding needs solar cell positioning as a reference point or base of sorts (didn't want to use the word constant) as part of her locating formula.

The island's not done with Claire