Factual error: In the beginning, James is collecting insects but it is cold enough for snow. Insects don't stay exposed to the cold like that.
Plot hole: Why do the scientists, whom are older than Cole, not remember that the army of 12 monkeys let out the animals? It was on the radio the same morning when Cole and Reilly were in the taxi on their way to the airport. It must have been a pretty significant thing in your memory especially if the death of the human race starts almost immediately after this event. They do not realise this until Cole calls the voicemail and explain the situation 5 minutes before hell brakes loose in the airport. Where were these scientists during this quite spectacular incident? Even Cole must have remembered something about this since he just went home with his parents after the shooting in the airport. The story about the fleeing animals must have been on most of the news networks that day, so why would the grown up Cole not remember this rather important piece of information from his childhood?