Yeah, at that part I actually leaned over to my brother in law and said "I think it would take a few more helicopters than that." I'm okay with fake physics in a giant monster/mech movie, as long as they don't look fake. There were three parts that screamed "fake" to me in that movie: the helicopter part, the part where they're swinging the cargo ship around and it's not just folding in half under the stress, and at one point a kaiju steps on a semi, which has a fraction of a second of resistance before getting crunched. That should have been like me stepping on a toilet paper roll.
Obviously incredibly minor problems overall, but each time it pulled me out of my suspension of disbelief.