Other mistake: As Viggo Mortensen narrates, it's been years since every crop and animal has died. Trees have been dead so long they're rotting where they stand and falling over with a stiff wind or slight tremor. Yet, in the woods, there are always fallen leaves on the ground which ought to have long ago decomposed, rain or no rain. Obviously, they can't sweep out the whole forest to make a movie.
Plot hole: 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.
Factual error: 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 super volcano, the additional CO2 would be accompanied by the gases from the volcano making the atmosphere even more toxic.
Plot hole: 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.
Factual error: Despite being on the Atlantic shore, the scene in the devastated amusement park opens with a shop of a sign saying it is Conneaut Lake Park. (You can also see the landscape on the other side of the lake in the background.) The scene was filmed not long after a fire destroyed several historic buildings at the actual Conneaut Lake park in PA. Since they used CGI to alter the actual park sign (which is at the entrance to the park and not on its boardwalk, I have to wonder why they didn't create a sign for a boardwalk park. (01:27:35)