Time paradoxes are the devil's snare for underemployed minds. They're fun to consider in a 'what if?' sort of way. Film makers and authors have dealt with this time and again in a host of films and television including 'Star Trek: First Contact', the 'Back to the Future' trilogy, 'Bill and Ted's Excellent Adventure', 'Groundhog Day' and the Stargate SG1 homage, 'Window of Opportunity'. Heinlein's 'All You Zombies' was written decades ago and yet it will still spin out people reading that short story for the first time.
In the case of Terry Gilliam's excellent film, '12 Monkeys', it's hard to establish what may be continuity problems versus plot elements intended to make us re-think our conception of the film. Repeated viewings will drive us to different conclusions if we retain an open mind.
Some, seeing the film for the first time, will regard Cole, played by Bruce Willis, as a schizophrenic. Most will see Cole as a man disturbed by what Adams describes as 'the continual wrenching of experience' visited upon him by time travel.
Unlike other time travel stories, '12 Monkeys' is unclear as to whether future history can be changed by manipulating events in the past. Cole tells his psychiatrist, Railly (Madeleine Stowe), that time cannot be changed, but a phone call he makes from the airport is intercepted by scientists AFTER he has been sent back to 1996, in his own personal time-line.
Even this could be construed as an event that had to happen in a single time-line universe, in order to ensure that the time-line is not altered...Cole has to die before the eyes of his younger self for fate to be realised. If that's the case, time is like a fluid, it always finds its own level or path, irrespective of the external forces working on it. It boggles the mind to dwell on this sort of thing too much.
If you can change future events that then guide the actions of those with the power to send people back in time, as we see on board the plane at the end of the film, then that means the future CAN be changed by manipulating past events...or does it? The film has probably led to plenty of drunken brawls at bars frequented by physicists and mathematicians.
Bonus material on the DVD makes for very interesting viewing. Gilliam was under more than normal pressure to bring the film in under budget, which is no particular surprise after the 'Munchausen' debacle and in light of his later attempt to film 'Don Quixote'. I would rate the 'making of' documentary as one of the more interesting I've seen. It certainly is no whitewash and accurately observes the difficulties and occasional conflict arising between the creative people involved. Gilliam's description of the film as his "7½th" release, on account of the film being written by writers other than himself - and therefore, not really 'his' film' - doesn't do the film itself justice.
Brad Pitt's portrayal of Goines is curiously engaging, although his character is not especially sympathetic. Watch for his slightly wall-eyed look in one of the scenes from the asylum. It's disturbing and distracting.
Probably a coincidence, the Louis Armstrong song 'What a Wonderful World' was used at the end of both '12 Monkeys' and the final episode of the TV series of 'The Hitchhiker's Guide to the Galaxy'. Both the film and the TV series also featured British actor Simon Jones.
'12 Monkeys' is a science fiction story that will entertain in the same way that the mental stimulation of a game of chess may entertain. It's not a mindless recreation, that's for sure.

The dudes at MST3K should see this dog of a film. It's basically about a dopey hack actor in Hollywood who can't land any acting gigs. And he has this strange obsession with the movie Taxi Driver. So what does this dumb actor do? He dyes his hair blonde and starts acting like a L.A. surfer dude in the naive hope this will get him acting roles. You'll laugh yer head off at so many of this movie's inadvertently funny scenes. Like when the actor dude's girlfriend is heart broken and sobbing and saying lines like, "How could you do this to me?" And why is she crying? Cos he dyed his hair blonde and became a surfer dude to get acting gigs. This movie makes no sense at ALL! The actor who played the governor on Benson is in this too and he plays a stereotypical right wing politician with lotsa dumb funny dialog. This movie will crack you up, trust me. You talking' to me?!