The "current" portion of the movie takes place approximately 7-8 years after the "disaster" happened that caused all plant life to die off. If all plant life had died off, there would be no dry grass shooting from the soil, nor dead grass lying on the ground especially with all the weather turmoil happening around. All leaves and dried grass would have decomposed in that amount of time. Furthermore, trees would not have dried leaves hanging from the branches.
In the beginning, the Man is shown to only have two bullets in his revolver. But when we see the front the revolver after he cocked the hammer and pointed the gun at the urinating gangster we see two rounds in the cylinder. The cylinder will rotate again if the hammer is pulled back, so when he fired seconds later the hammer would have hit an empty chamber.
The Man is looking for gasoline in an old station but by that point, he'd have already learned that any fuel he might have found would be pretty much useless. Gasoline only has a "shelf life" of about six months. This can be extended by storing it in a vacuum-sealed container but even then, it certainly wouldn't last for years.
When the Man was at the gas station he tried pulling the trigger on one of the gas pump nozzles to see if it had any fuel left. However as the power grid is not functioning the pump would not work either, so using the nozzle would not be a accurate way to see if there was any fuel left. The only way to see if there was any fuel left would be to check the underground holding tanks.
If, as the film proposes, all plant life is dead, then human life would have soon followed it. SInce plants filter carbon dioxide from the atmosphere, then a lack of plants would allow for the increase of that CO2. And since the the unknown disaster appears to have been the result of a supervolcano, the additional CO2 would be accompanied by the gases from the volcano making the atmosphere even more toxic.
The pistol the man carries with the boy (supposedly the same from his home) is a small caliber revolver. The pistol that the man and woman 'talk' over and even show the last 2 bullets is a large caliber revolver. This is clearly visible in each situation when the barrel is visible.
A disposable Bic-type lighter cannot be used as a candle the way the Man does on multiple occasions. Within about 30 seconds, the metal would heat up enough to melt the plastic and possibly cause a painful accident.
Despite supposedly being deprived of food, neither of the main characters (nor most of the minor characters) seem to display any signs of malnutrition. They both have all of their visible teeth, their stomachs are not distended and they seem to have a large amount of energy to travel by foot over lengthy distances.
The sheer quantity of people that the man and boy encounter is absurd. If the majority of people worldwide are deceased, then the Americas, where the film is set, would be nearly depopulated. They should have not encountered many, if any, people simply because the survivors would either be in isolated town or cities or they would be holed in remote rural areas. SInce the two largely avoid the former and the size of the latter precludes easy visitation, they shouldn't have run into anyone for most, if not all , of the film.
When the Man dies he is covered by the gray blanket and has something with a buckle beneath his head. When the Boy comes to say his last goodbyes, the Man is covered by the colored blanket and his head is on sand. It would appear that either the Boy or the Veteran has removed the gray blanket from on top of the Man and wrapped the colored one (which was underneath him) around him.