Other mistake: Right after Otachi sprays acid, Gipsy reaches in its mouth to pull its tongue out, but doesn't get affected by any.
Factual error: When the fisherman in the beginning locates the supposed island on the radar he says it's three miles away. The Kaiju (island) then crosses the distance to the boat in about ten seconds. This would mean that the Kaiju swims at a whopping 1080mph (1738 kph) which equates to about Mach 1.4.
Continuity mistake: The crew of Striker shoots Leatherback in the eye, but in the next scene, it's fine.
Continuity mistake: When Chuck Hansen is sitting at the dinner table arguing with Raleigh he is bareheaded. He stands up and in the next shot he has his baseball cap on. He had no time to put it on at all. It seems to have spontaneously appeared on his head.
Chosen answer: Most likely they only use it when they know they have a guaranteed shot and won't waste it. It can't be reloaded that easily. Like having one bullet to kill a zombie vs a sword so go for the sword save the bullet it's more valuable. That's typical military tactics. Possible firing whatever weapons could cost a ridiculous amount of money just like missiles do. It's not exactly like Yeager weapons were mass produced they are all different. Last reason is reducing extra casualties by making sure they don't miss when they fire or making firing weapons the last resort. And just for the movie's sake it would be boring as crap if they just blew the heads off in seconds.