Factual error: During the scene where everyone runs outside, the Statue of Liberty head crashes into the street. The head is scaled too small and its size can be compared to the people taking pictures. In real life the statue head is large enough for people to walk into (17' from chin to cranium).
Factual error: In the first scene where the Army attacks the monster, the first tank that rolls by is actually a British FV-433 Abbot self-propelled gun made during the Vietnam war years, not an M109 Paladin which most people believe. (Paladin has a longer gun barrel, and has rear turret overhang.) And a few seconds later we see, next to the M1 Abrams, what appears to be an MLRS system firing, but is actually some kind of truck with a multiple rocket launcher, much like the Russian BM21, not the U.S. tracked MLRS system or the M1097 Avenger (which I originally thought it was).
Chosen answer: The actors and crew were kept in the dark as much as possible, unless the information was needed for their performance. They didn't know what the parasites looked like until they began filming the subway scene. Actual-size, realistic puppets had been made for filming but were decided to look too artificial and slow on camera, but it gave the actors a chance to see what they would be running from, how their jaws and legs worked, etc. As for the main monster ("Clover"), actors would only know what was in the script and what the director told them.