Factual error: The coastal wall in Sydney is shown as being inside the Sydney Harbour (right next to the Opera House). But Sydney Harbour is not on the Pacific coast but a part of the Parramatta river, several kilometres from the ocean (where the wall should have been). So the wall is either not shielding the northern part of Australia or (more likely) the producers decided that the audience cannot tell that it is Sydney unless we see the Opera House.
Factual error: During the Hong Kong battle, one of the Kaiju disables the Australian Jaeger and the base by emitting an EMP blast. Becket claimed that the Gipsy Danger was immune because it had a nuclear core and was therefore "analog". Being nuclear powered has no bearing on whether a machine is analog or not, and the EMP would certainly affect all the electronic circuitry needed to control the Gipsy.
Factual error: Gipsy Danger's fist bumps into an office table as it screeches to a halt. The Newton's cradle on the table has an impossible reaction. All of the balls would simply sway in parallel, and not the 'classic' reaction displayed in the movie.
Factual error: When the Kaiju "Trespasser" hits San Francisco at the start, F-22 Raptors attack it at the Golden Gate Bridge. The Raptors each fire two machineguns - but the F-22 carries only a single M61A2 cannon.
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.
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.