Spoilers I guess.
I read about the Coney Island scene before I saw the movie and watched the horizon carefully, and yes, there's a long, grayish object that falls into the ocean. It could have been the monster, or it could have been a satellite that is reported to have fallen into the Atlantic Ocean on the Targuato website (as part of the viral marketing for the movie). Either way the origin of the monster is pretty ambiguous. Which I love.
Also I'm with you about the bridge thing. The subway scene also had me wondering why in the world they'd want to hide under something. I was sure I'd see a huge foot coming through the ceiling at some point.