Corrected entry: Twelve Monkeys may be one of the most subtly subversive commentaries on the Catholic Church (or Christianity in general). The themes and images in the movie, from the prophecies to the Doctor's claim that psychiatry is "the new religion" to the Mary and Jesus like pose in the end, suggest an underlying religious message. Consider the fact that Cole was "sent" in order to "save" mankind from death (brought by a charismatic gentleman with red hair, no less), resulting in a future in which the elites of the establishment control the "cure" and determine who will "ascend" to the world above. Other allusions include the "army of the twelve monkeys" (re: twelve Apostles), the word "Chris" on Cole's shirt (only missing one letter), and Cole's visions of his death. (One more: Cole's first name begins with a "J." Think initials.)
Corrected entry: Katherine's phone message that is responsible for the hypothesis about the Army of the 12 Monkeys is left as a direct result of her experience with Cole, and at the same time what leads to him being sent back in the first place. Well, if that message is there all along, then why isn't the one Cole left at the airport contradicting it also present from the beginning? It should have created a paradox, as it would have stopped the investigation into the Army before it started, hence the first message would never have been left.
Corrected entry: In the second half of the film James Cole, unrecognisable with all the clothes he's wearing, his face covered - Dr Railly, herself, for the first ten minutes, doesn't know who it is that has kidnapped her and her car - is somehow known to the police. The authorities, her friends, all say it was James Cole who kidnapped her, but they couldn't have, it was impossible. Also, Dr Railly's car was away from everyone at that time - she was leaving the party early, so they could not have known who he was, but they do.
Corrected entry: The discussion about the bullet recovered from Cole's' leg being an "antique" and fired some time in WW1 does not make sense. Age of a bullet cannot be determined like that, as I have a rifle from 1912 myself, the ammunition for which I own is old ex-military stock of a similar age. If I fired it now, no one would say the bullet was fired in 1912. Also, having moved forward in time with Cole would make the bullet "brand new" looking, it hasn't tarnished for 80 years in the open.
Corrected entry: When Cole forces the doctor to get in the car, she drops her purse but they still get in the car and drive off. Later on in the film she gets her bag out with the stuff she dropped in it.