Zombies are a popular horror phenomenon, relatively newer than many of its fellow genre-defining horror creatures, such as Vampires, Werewolves, or Mummies. As their inception is rooted in an age where science is a notably bigger part of everyday life, so too has the evolution of this genre swayed the development and understanding of the zombie towards a less mysticized version, to one where many of it's traits mimic, or can at least be understood in ways consistent with science. Still, both versions of the creature have inconsistancies, or traits that seem to either defy reason and science without further clarification, and their depiction in movies and television shows often defy logic and basic science.
Problems with Theory
Slow Moving Zombies
Slow moving zombies, who could attain at most one hobbled pace every 1.5 seconds, were the first zombies in film or literature. In the Vodoun religion, their creation was clearly supernatural. As it is often seen with supernatural concepts, no attempt is made to explain how the effects and events of the mythos coincide with the scientifically understood world - the supernatural simply exists out of the realm of modern science.
George A. Romero, while bringing the myth to a grittier, and less spiritual landscape, chose a scientific foothold that is largely unpalatable in regards to modern understanding of physics. The Living Dead are re-animated when a mysterious radiation cloud from space penetrates our atmosphere, and saturates a human corpse - both newly, or long dead - giving them the ability to do things that a living person could do, and the human-consumption behavior that has made them so famous. Romero himself has stated that while a bite from a zombie would be fatal, any fatal wound imparted on any human while the Earth is in this radiation cloud will reanimate the deceased in due time. While there is evidence to suggest radiation can mutate life, there has never been any scientifically valid indication that it can reanimate even the simplest organisms after death.
Max Brooks's Solanum-based zombies are a major step forward in linking the mood and behavior of the Romero or Vodoun zombies with a more scientifically comprehensible framework. Zombie outbreaks occur when the rare virus Solanum is introduced into a human. The virus is so rare, that it has never been studied, or even identified until World War Z.
The composition of Solanum is largely outside of scientific understanding, both in its own universe, and as described to us in Brooks's works. Because an ample supply of Solanum can be implied to be stored in secure facilities in Brooks's universe, one can validly say that an eventual conceptual bridge may arise through continued research, linking Solanum's inexplicable properties to our current understanding of biology and organic chemistry. Likewise, it is equally valid (and perhaps, even suggested by the author, given that flooded ancestor shrines and cemetaries submerged under the Three Gorges Dam reservoir are implied to be origin of the World War Z outbreak) that Solanum is simply a name given to a entity supernatural in origin and properties, and no amount of scientific investigation will ever produce enlightenment. Ultimately, such topics are left open for debate and the imagination.
Solanum does not require oxygen, leaving no need for a respiratory system. It is also makes the internal organs highly gelatinous, and resistant to the pressure of the ocean depths. Brooks, as other authors have done before, made his Zombies' appetite unrelated to the need for sustinence from flesh. They do not draw energy or nutrients from feeding on humans or anything else. They will continue to hunt, bite, and pass flesh through their mouths, even if they are reduced to only a head whose brain is still intact.
Simultaneously, this allows close combat and point blank firearm discharge to be as practical for zombie combat as it is fun for most zombie enthusiasts to imagine engaging in. Without this solidity, infection through blood spatter would all but rule out any physical contact with the undead. Lastly, Solanum is extremely toxic to all living things, which staves off decomposition and animal attacks, and somewhat resistant to oxydization and corrosive materials. How a virus could have these properties (as well as the energy for years worth of locomotion) is a difficult thing to imagine ever occurring.
Fast Moving Zombies
Fast movers (in most portrayals, Infected is a more accurate term), offer notably less conceptual problems, and this is not coincidental in the least, as they were most likely created both as a modernization of the traditional zombie myth, and a way around some of the conceptual issues previously mentioned. Since the viral spread of the Zombie condition is an inherent theme (more so than Vampires or Werewolves), many authors have independantly used the idea of a literal virus (albeit with properties so extreme and unprecedented, they could only be accepted in Science Fiction) to put a fresh spin on the genre, and partly remove the supernatural aspect of the creature, making the myth feel more plausible.
Fast moving zombies still have their psychology and biochemistry radically altered, sometimes in mere seconds. A chain reaction of this speed is not unprecedented in the nervous system (where impulses travel at several hundred miles per hour), but is inconceivable at a celluar level (meaning a zombie bite on the toe may affect the brain eventually, but it could not make all bodily fluids become instantly overrun with the virus). Even if the virus sends a signal to the brain to accelerate the heartrate, transformation into an Infected with the capacity to transmit the virus would still take minutes.
Problems with Depiction
Aside from the workable (or unworkable) theories on how various zombies come into being, there are many problems in zombie media dealing with plotlines and depictions in movies and tv shows. One of the most obvious problems has to do with the relative ease of killing them by destroying the brain through the head. From stabbing through the face with a shovel to forcibly pushing an arrowhead through it with your bare hands, penetrating the skull seems easy. In actuality, the skull is one of the densest bones in the body and is extremely difficult to actually get through. Many edged weapons that are shown to just push through would, in reality, not even break through and would only push the head forward harmlessly. Blunt force and improvised weapons meant to smash the head require more work to be effective and may sometimes not even work, at least in a single blow.
One problem with slow zombie plots is their depiction that they are unstoppable and will have almost no problem consuming the Earth. Enough slow zombies could be basically unstoppable to a group or survivors, but their slow speed and slow rate of turning people that are bitten make it very difficult to assume that the zombies would be the ones being overwhelmed in the early stages of an outbreak. With a virus like Solanum, where it requires a zombie to bite a person, then take several hours to die and turn, the slow transmission rate would likely allow people to destroy the undead before too many people turn. The virus spreading out of control depends on ignorance of the threat and panic once it is realized. The length of time required for a slow zombie to move and turn others would likely give enough time for people in an area, regardless of population, to be able to figure out what they need to do to wipe them out before undead numbers get out of hand. This is more of a problem in scenarios where anyone who dies of any reason reanimates, thereby dramatically increasing undead numbers, but the slow pace of zombies and transformation times could still leave a society enough opportunities to take necessary measures (although still dramatically changing their way of life).
Another problem with slow zombie plots is that military forces will always be overrun by undead hordes. True, they are enemies unlike any other an army has fought, but stories depend on soldiers being too horrified and demoralized to effectively resist. One point is that they would not be able to concentrate fire on the head, or that they are too well trained to refocus to the head after being trained so much to hit center-mass. This is frankly an absurd notion, since if a soldier is trained to fire at a point accurately it would not be difficult to aim about a foot higher if they know that is the only way to kill their enemy, although this significantly decreases firing range. Modern soldiers carry almost 100 pounds worth of gear, which reduces endurance and maneuverability, but any soldier knowing what this threat is would know immediately to shed what equipment is not needed for zombie combat to reduce weight. Well trained commanders are taught to improvise to accomplish their mission, so it would not be hard to come up with tactics that would make it easier to kill the undead while going to or creating a firing position inaccessible to slow and dim-witted zombies.
For fast zombies, the ability of both the infection and the infected to spread so quickly actually poses problems for the scale of the infestation to reach apocalyptic proportions. While they would be very effective in confined spaces and urban areas, a fast mover will likely burn out his reserve of energy (which is considerably superior to, but still in the same league as an ordinary human) well before it walks across miles of terrain. And very few vehicles with infected aboard will reach their destination. Quite simply, the greatest tool of viral infection is a delayed incubation period, allowing it to move to new victims and new areas before it is detected. While an attack of infected may be fiercer and more intense in the short-term than an attack of an equal number of zombies, the infected ultimately acts to burn itself out. Long-term duration of the infected is also a point of contention, in that there is virtually none. Unless they know how to scavenge and hunt (which they shouldn't, as their premise is they only seek to infect other humans), an infected human body should only survive for 3 days at the most; they should die within minutes from blood loss if they're bitten in a vital area, hours if they sustain combat wounds which aren't treated, and a couple days from infection of an exposed bite wound, exhaustion from unceasing adrenalin use, and dehydration.