“Send more cops!”
I disagree with that. I think what we saw was a cleanup happening in a rural, low population area. Certainly possible for local containment. However, as indicated by the events at the beginning of Dawn, zombies continued to be a problem in areas of higher population, growing in number as people refused to let their loved ones be turned in for proper disposal.
It’s been a while since I saw the original Dawn, but I seem to recall them seeing what looked like “clean up” scenes on the ground as they went over the rural areas in their attempt to flee the city.
How easily would the Army be zombified? I mean, does kevlar stop human teeth? I know they aren’t made to protect people from being stabbed, but human teeth aren’t the longest or sharpest teeth by a long shot. I think a leather jacket would be fine. Find a riot helmet to cover your face and head and you’re pretty set.
A soldier in some kind of full combat protective gear (there’s an acronym for it I can’t remember) would be a tough nut to crack, for a zombie’s wimpy mouth anyway.
While I agree with what everyone else said above regarding zombifying humanity, this was my question regarding the vampire movie Blade, in which the villain’s big plot was to turn all humans into vampires. My reaction was “And?!” 
It’s a general weakness of lots of “genre” fiction that the military/police are never useful, often for fairly weak or unexplained reasons.
For instance, in the Buffyverse, it’s generally accepted that police/military would, if unprepared, be totally helpless against just about anything supernatural, but at the same time one of the most utterly super-top unstoppable supernatural creatures, pretty-much supposedly unkillable, gets totally wasted by a rocket launcher. Which is FAR from the most powerful weapon the military can lay its hands on.
Similarly, why is the military so useless against, say, Godzilla, or the monster from Cloverfield? In neither case is the baddie depicted as magical, and I don’t care how big and ugly you are, modern military weapons do SO MUCH damage that, purely from a physics perspective, big nasty monsters should not be shrugging them off.
But when there’s a story in which Our Heroes (not meant sarcastically) are the protagonists, it’s generally essential that the authorities not save the day.
What I don’t get is the whole zombie fetish thing. Let alone how to fight them off. Weird.
FINE.
Good luck with the zombie apocalypse.
My biggest objection to the zombie apocalypse is that very few people should be converted to functional zombies. Many/most that fall to the horde will be completely or mostly consumed. I would expect a limited number to get bitten, then escape and convert to something actually dangerous.
Of course in the original NOTLD it was radiation, so there’s that.