Eh, I don't take zombie apocalypses with any serious grain, but here's some flaws in these arguments:
1) Too Many Natural Predators, including insects that would render rotting flesh useless pretty quickly.
This assumes eating the flesh of the infected wouldn't cause a blight on the consumer. Also, zombies who congregate in herds would be more than a vicious match for most 4-legged predators.
2) Zombies don't like hot weather: dead bodies bloat within weeks due to stomach gases and start exploding, and in extreme heat they would shrivel like raisins.
This assumes a lot about the physiology of an undead corpse is the same as a dead corpse. I can think of at least one reason why it isn't.
3) Zombies don't like cold weather: frozen meat becomes rigid
Fair enough, but what about summer months, and global warming and thawing? If you don't have a sustainable food source and heat in a cold climate, you'll be pushed south where there's plenty of zombies looking for a fresh food source.
4) Biting isn't a good way to spread disease...
Let's not forget, not all zombie outbreaks are caused by disease. In Romero's films, you die for any reason and come back as the undead (assuming the brain isn't destroyed).
5) Zombies can't heal: every time a zombie fell or was injured they break bones and lose body parts without anyone there to patch them back up, and the human body is pretty weak, many household items could be used to easily kill a zombie like a shovel, bat, hammer, sledgehammer, 2x4, chainsaw, etc. If someone broke in your house to kill you right now what would you use to kill them with? Whatever comes to mind are your zombie weapons.
True, but zombies don't have most of the same kill points or have the fear or instincts a living assailant would have. Essentially you have a killing machine with a single-minded goal and a limited and semi-armored kill point. Close-Quarters combat is always gamble with one, as their teeth pretty much just have to scratch you and you're screwed. A bat, shovel, 2x4, isn't the best option against multiple zombies if you're going for a kill. A hammer is a extremely dangerous if you're not getting a one hit kill or swinging from behind as it only extends your reach by a foot or so. Most people would have trouble wielding a sledgehammer without some practice and even then, it's a gamble. Chainsaw is a great way to get infected blood all over you and immobilize you while you try to hack through a bone or even a weak point like a neck (and it's super loud). And hacking off the limb of a zombie isn't going to phase them a bit.
6) Zombie-Proof Barriers (and zombies don't use tools)
Zombies do have limited use of bludgeons, and some cases, fire arms, see Romero's Land of the Dead and others.
7) We have a lot of guns: there are almost 15 million hunting licenses in the US [nssf.org] and that doesn't count people with guns that don't need a hunting license like handguns or the military and the police. There are 300 million people in the US [google.com] so even if the entire US was zombies except for the 15 million with hunting licenses each person would only need to kill 20 zombies. That doesn't sound too difficult.
Unless you have a well-stocked personal arsenal and armory (and I'm sure some people do, but not most), you'll run out of ammo eventually, or at least be limited to what you can carry, when scavenging, and in that case, you'll have to deal with other armed humans, where all bets are off. Also, gunshots can be more dangerous than a single zombie as it's like sending up a flare to your location, to all the other zombies.
8) Zombies feed and reproduce with world's #1 predator: Imagine if every time you wanted to eat something or have sex you had to first kill someone but everyone knew you were coming? How long do you think you would last? Probably not very long, someone would kill you off or you would starve to death quickly, but that's the life of a zombie.
Eh, again, this assumes zombies breed purely from a viral outbreak, and not something more endemic arising from a state of death. In that scenario, everyone is a zombie once they die, and sentimentality always gets someone eaten. But nowadays, zombies are always some kind of viral outbreak, which makes them a more resolvable target. Credit Romero once again for painting the bleaker and more hopeless landscape, and the best Zombie films (Night, Dawn, Day, Land).
Man, am I bored at work...