Audio problem: When the Statue of Liberty's head strikes the top of a distant building before landing in the street, sight and sound are simultaneous. There should have been an audible lag in the sound due to the speed of sound being only about 1000 feet per second. The absence of this lag would be acceptable in most movies but is inconsistent with the amateur home movie theme of Cloverfield.
Audio problem: Right after Det. Corelli finds the limerick in her apartment, she pulls out her gun and there is a distinct sound of what's supposed to be her cocking the hammer on her pistol. However, Det. Corelli (along with all the other cops in the movie) uses a Glock semi-auto pistol, which does not have an external hammer that can be "cocked." The sound is added artificially, likely for dramatic effect. (01:06:30)