I think that it is the Flight 828 tailfin. Although, it is not the "same" one which landed in New York 5 years after its scheduled landing. For two seasons, the characters have been thinking that it was some "electrical storm" that caused the anomaly. But, a better explanation (considering that the show is Sci-Fi) would be that it wasn't an electrical anomaly; it was a gravitational one.
So, in my theory, there was a huge gravitational disturbance created near Earth (or our solar system) which caused the space-time fabric to overlap more than it should. The characters were unfortunate enough to get trapped in such a "fold" (one may think it like the ups and downs of a wave, but stuck together). When they moved across the fold, for them "time" had not changed, but for those who were not in this fold (or the wave) had moved forward in time 5 years.
5 years (as of the original timeline) later, the pilot tries to run simulations of the "electrical storm", but does not understand it. So, he takes matters into his own hands and despite of attempts to stop him, he manages to take the plane into the same storm. At that moment, it seems that the plane crashed or exploded mid-air when a loud thunder is heard in the background. However, here is where the tailfin theory comes into picture.
Considering that the "electrical storm" was actually a gravitational anomaly, the pilot was able to again travel through time bringing the plane back to the time when it was landed (notice that this happened in a matter of months after the landed and hence the gravitational ripples may not have ceased). Now, the plane was at two different points in the 3-dimensional space (the one which we can perceive) but at the same "point" in time (looking at the universe as a higher dimensional object (x,y,z,t)). This would have made the two copies of the plane "entangled" (here comes the Sci-Fi part for nobody knows how entanglement of particles work in reality and whether or not it is really possible). Just when the pilot was about to know what happed, the engine died and the plane exploded mid-air. Since the two copies of this plane were entangled, the other copy sitting at the airport (where it was being studied) also exploded in a similar fashion.
Since the weather was not exactly good, there were no ships/boats in the area where the plane had crashed in the sea. Years later (towards the end of Season 2), fishermen find the tailfin of this plane.
So, in a way, it was truly the tailfin of Flight 828 just not of the same time!
PS: The gravitational anomaly would also explain similar happenings in other parts of the world. The ripples in space-time fabric were travelling and getting less intense, thereby making people travel through less time (example, Zeke, who travelled only a few months in time, or the other person who drowns but somehow survives; he travelled for even smaller amount of time through time)!