Goofs

A man sets himself on fire outdoors, where there is supposedly not enough oxygen to breathe. For humans to have problems, the concentration is going to be lower than the minimum to burn fuel.

The death of all plant life would not immediately eliminate the vast quantities of oxygen already in the atmosphere. In addition, as others have commented, people would starve to death long before they breathed up all the oxygen in the atmosphere. In addition, even if there were somehow an oxygen shortage, a little bit of electrical current in water (freely available and abundant in the ocean) can create oxygen easily.

In 2067, when all the plants have died out and no longer produce atmospheric oxygen, some people will apparently have 'synthetic oxygen rejection sickness'. Oxygen is oxygen - it's an element; if you change its chemistry, you've got a different element. Ergo, it is impossible for people to get sick from breathing 'synthetic oxygen', whatever that is. Also, if there are no plants, people would starve to death for lack of livestock or vegetables, unless they resorted to cannibalism, which wouldn't last very long.

Ethan finds the skeleton sitting upright with the skull intact. The skull would have detached from the rest of the skeleton after the decomposition of the skin, flesh and muscles.

Over a period of 400 years, bones in the open in a humid climate would completely decompose. Maybe in a arid environment they would last but not in the condition universally depicted in this film.

While the effects in this movie are pretty good, there are a couple points where they were lazy with the sound effects. It's very distracting to hear Half-Life/Counter-Strike sound effects at 1:30:51.

Two different spellings ("Chronicle" and "Chronical") appear throughout the film in print and in the English subtitles.

They are sending someone 400 years forward in time. With no clue or anything in what kind of (unfriendly?) environment he will arrive. And they don't give him any food or drink for the first days in the future? So he has to eat some berries which are unknown and turned out to be very poisonous.