None of what happened in the movie is real
Cole is in fact a schizophrenic patient, but the only parts of the film we see happen in reality are the scenes where he is in the hospital talking to psychiatrists. Both the "present" and future worlds were artificially constructed in his head. As a child, he was traumatized by an airport shooting, which in turn led to him constructing a world in his head. The psychologist Dr. Railly is real, and has been helping Cole for some time, but she is only going along with his delusions and occasionally having a bit of fun along the way (being able to leave a prank call about the Twelve Monkeys). Ultimately, Railly's help has started to bring Cole back into reality, but he is still under the delusion that he is a time traveler and requires her assistance, but occasionally he experiences a temporary relapse (his apparent returns to his own time). The climax is ultimately Cole coming to face the source of his delusions by experiencing the shooting again and confronting his delusions which, though not shown in the film, finally bring him back into the true reality.
The 2015 Series
Cole will get trapped in 2015 by the end of the first season.
The psycho band of scavengers introduced in S 01 E 03 will succeed in locating and storming the compound led by Jones. In the chaos, the time machine will somehow get damaged and prevents Cole from splintering into another time period.
The Witness is Cole from an alternate timelineGiven that both his organization and Cole use the same phrase "set right what once was wrong", and that we do not actually see the Witness at any point, the Witness is a Cole from a different Bad End future, who was sent back to recover the plague. Unfortunately, this Cole has slightly more of an advantage (but pretty similar methods) to the Cole who we are following.
- Jossed. The Witness, as revealed in the Season 2 finale, is Cole and Cassie's son, who was conceived in an alternate timeline.
- Double Jossed in the Season 3 finale. The actual Witness is Olivia . . . and she is as surprised by this as anyone.
Cole will discover that the plague was a result of a Stable Time Loop.
His own actions in the past will turn out to have set the plague and/or its instigators in motion, forcing him to splinter one final time to stop the splintering program before it can get started.
The body in the night room that the virus was originally isolated from was one of Jones's previous attempts.
They inadvertently started the plague themselves through Timey-Wimey Ball. Maybe instead of sending this guy back through time he got pushed into an alternate universe where the plague didn't happen and oops!
- As they carbon dated the remains to 1,000s of years old, this seems unlikely. Even a jump back to 1987 was difficult to achieve. Although it was interesting that Cole seemed to have a similar headache response to being close to the remains as he does to meeting his other selves, which did make this troper wonder...
- Seems easy enough to write around - damage to the machine and/or a partial understanding of how it works sends the subject (or parts thereof... meaning they would just assume it was another failed attempt) to an arbitrary, random date in the past, but kills them in the process (say, embedded them in ice where they are later found).