The mention of "maneuvering erratically" and taking off without headlights seems to further advance the simplest explanation... but everyone loves a good conspiracy theory.
I would think there would be an oil slick, and some floating debris. There's a lot of stuff in an airplane that floats. Surely these things would be spotted by air or satellite.
Think about a comparable problem, finding shipwrecks on the ocean floor. The ocean floor is vast, the shipwreck is tiny, modern techniques rely on looking for the debris trail to focus the search for the shipwreck itself. But in these cases the advantage of the shipwreck remaining in one place and relatively unmodified are completely lost for debris on the surface, and there is far less of it. The oceans are big, the floating bits of a 727 are small.
Now imagine the same thing without a good idea of where it went down. The ocean is a pretty big place. Maybe some debris will wash up on a shore somewhere, but that might very well be half the world away from the crash site.