Is there a way the zombie virus can spread around enough without every single armed force on earth being totally incompetent?
Actually, even with competence an actual just like the movies Zombie Apoclypse would at least surpise or catch unaware initial attempts to stop it I would think. I mean almost everyone knows how movie zombies work and shit, but seeing it start to happen in real life is unreal enough to be dangerous on it's own. In fact the cultural awareness of movie zombies might even cause problems.
How is this patrol sent to investigate something in the dark in the middle of an urban center going to tell the difference between 20 bored college kids doing a zombie walk too drunk to respond or 20 actual zombies shambling towards them? It seems stupid and silly but do remember, at one point there was an accident where a Russian garrison mistook some radioactive powder for talcum powder since they appeared very similar and in similar containers. It sounds stupid but when something is routine it dulls the senses.
But afterwards, actually containing a zombie outbreak shouldn't be a huge undertaking after it's realized what they are and that it's ACTUALLY happening. Unless it's a Romero style the dead come back to life no matter what thing. Then everyone's screwed anyway.