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 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.
Throughout the series, characters regularly start and drive abandoned cars. In real life, over the several years covered in the show, the gasoline in abandoned vehicles would have degraded significantly, with many of them being unusable.
Throughout the last few seasons, there have been references to Eugene being able to make "bullets" in a machine shop he found. That's an incorrect reference to what is actually a "cartridge". A cartridge is actually the assembly of 4 components: a brass casing, a lead bullet (typically encased in copper), gun powder, and a primer. Although you could argue that a lead bullet could be cast with the correct bullet mold, there has been no mention of them having one for the assortment of calibers used in the show. A machine shop is no use for casting bullets - sufficient raw lead to melt in a furnace and suitable molds are what's needed. Machining casings would be incredibly difficult in a normal machine shop, if not impossible. There is also no mention of obtaining the copious amounts of gunpowder and primers that would be necessary for constructing workable cartridges. Hand forming actual bullets would be tedious, time consuming, and produce highly inaccurate cartridges that wouldn't be effective beyond 25 yards. There is no way that primers could be constructed without highly specialized machinery, raw materials, and the correct flash powder which isn't even sold in gun shops.
A lot of the time characters kill walkers by pushing a knife up through their bottom jaw. Most of the knifes they use are not long enough to reach the brain and so walkers are essentially just being stabbed in the mouth, yet this seems to be an effective method.
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.