Throughout the series the sound effect of a gun being cocked is used incorrectly. Often when a character draws a pistol the sound of a hammer being cocked is heard, but often the gun being used does not have an external hammer, but a internal hammer known as a striker plate (like a Glock). Or even with guns that have external hammers, like revolvers, we hear them being cocked but when we see the gun the hammer is still clearly uncocked.
Most characters look over fed and none suffer from the medical, dental, hygiene or hunger challenges they should be facing. Realistically, people should be tired, bony, dying of simple infections, minor injuries, colds and the flu.
Many characters appear to be overweight or of healthy size. This makes no sense considering the constant search for dwindling food supplies.
The zombies' organs still work, as shown when Rick and Daryl cut open the walker looking for Sophia. Blood would need to be pumping through the veins in order for this to happen. Blood pumping would not allow the zombies to decay.
The fuel they are using in their vehicles if it was an ethanol blend, would have degraded significantly in just 12 months, and this show takes place over a number of years, by which time the fuel would be unusable, and yet they seem to be using it without issue.
There is no clear reason why Michonne's technique of walking with two zombies on leashes deters other zombies from attacking her. By this logic, anyone walking around amongst the zombies, regardless of whether or not they are covered in zombie blood and guts, should be safe, so long as they don't do anything to draw attention to themselves.
At various times throughout the first two seasons, some walkers were seen by the characters to remember items and places important to them. In addition, some walkers could think enough to use tools (such as a rock to break glass), know that turning knobs can open doors, and were agile enough to climb high fences. Subsequent seasons, the characters behave as if they have complete amnesia of such significant experiences with the walkers.
Throughout the series, Carl physically ages much faster than anyone else. Neither a baby (Judith) nor a boy (Sam Anderson) who would be the same age as Carl in the time frame, show such accelerated aging. Not only is there is no explanation, all the characters act oblivious to it. Despite Carl's slow brain development, he is still viewed as being much older.