Continuity mistake: When Sam is loaded onto the school bus by his mother, her work friend 'Laura' is on the bus. Later, on the bridge, she seems to have disappeared.
Continuity mistake: When Juliette Binoche is running for her life in the tunnel near the beginning of the movie, when the running starts you can see all men run pass Juliette and then she's the last runner. There's even a shot when she's looking back at the leaking water and is last, with no-one behind her. A second later she's in the front of the running group.
Continuity mistake: When Godzilla collapses to the ground before the nuke goes off he is right next to the water, but when they show him the next day he is in the city, about a quarter mile away from the water.
Answer: Because detaching them and reattaching them would have taken time, which they didn't have.
But, after the crash, they remove the warheads and transport them by helicopter and leave the boosters behind, as they only need the warheads.