Revealing mistake: When Bob and Ben prepare to gas the ant nest, an ant appears below them. But its legs move too slowly, compared to the speed in which it appears; it rather looks like it is driving across the ground on (hidden) wheels.
Revealing mistake: When the giant ants' nest is taken under fire with bazookas, it can be seen that the back-blast jets are just inserted, e.g. the 'zookas are not actually fired. Also, there is a cut between the 'firing and some of the explosions visible in the same frame.
Answer: Like the General said, the less people that know about the ants the better. They were a special task force assigned with the equipment and deputized to use any and all measures to stop the ants. Since the movies was set in the 1950's, James Arness and James Whitmores were most likely veterans of WW II and Korea.