The taxi driver is Zeus, or Hades, or a collective apparition of the Greek godsAs is pointed out within the film itself, the name of the ship, Aeolis, is a reference to the figure of Greek mythology. His father, Sisyphus, was condemned - by Zeus, by Hades, or by all the Greek gods, depending on how you interpret the old myths - to forever roll a boulder up a hill, only to see it roll down again, a fate clearly intended to mirror Jess's imprisonment in the time loop. Zeus, or Hades, or whichever god/gods inflicted this punishment upon Sisyphus, clearly felt that Jess deserved the same punishment for abusing her son; so they created the time loop, then manifested themselves in the human world in the form of the taxi driver in order to lure Jess into the loop's beginning. Poor Jess is, in other words, doomed to repeat this experience for eternity.
Heather doesn't existHeather is listed on the main page under What Happened to the Mouse? because after she falls off she's never seen or mentioned again. If you go with the theory that Jess is in purgatory and this is her punishment then it's possible Heather only exists in purgatory (for whatever reason) and vanishes after she's no longer relevant.
Jess can break the cycleFollowing the Cab-Driver-is-Zeus/Hades/Death/Whatever theory. Jess' labor is Sisyphean, but the powers that be may be merciful. All she has to do is return to the cab instead of restarting another cycle, thereby honestly fulfilling her agreement with the driver. But to do that, she'd have to finally accept her son's death. As long as she can't let go, she's doomed to keep reliving the day.
Heather survivedFollowing the theory that the group died in the capsize and are now in hell/purgatory, Heather going missing may indicate that Heather survived the accident and therefore did not die and is not suffering the loop. Her occurrence in future loops from Jess' perspective may indicate she may be in a coma periodically entering the loop, or is simply a projection of Jess' hell/purgatory.
There is part of the cycle we aren't shown (or more than one cycle)And more than just single Killer Jess. During the movie we watch all the steps Jess takes up until being tossed overboard as Killer Jess by her "earlier" self and then restarting the circle after Timmy's death. But when Jess is next to dying Sally, she overhears sounds of fight and watches as another version of herself brutaly murders Killer Jess 2 with an axe (this version of Killer Jess is unmasked), after which she tosses her overboard. Since we never learn how the hell that happens, there is some part of the story not shown within the film. Also, the Jess we watch throughout the entire story is the Jess that shoots Sally and Downey in the theater, but we never see how and from where comes the Jess that kills Downey and Sally with a knife. This is obviously part of the Stable Time Loop, but it's never explained how it even happens and from where comes this version of Jess. We also never meet the Jess that successfully kills the Unmasked Jess, but she still wears her blouse, so it's (theoretically) possible to track when her loop divergents. If it divergents.
- There are also two versions of Victor's death. One is killed by Jess in self-defense, and then there is the one fend-off by a shotgun-totting Jess (this one is eventually killed by Unmasked Jess). In fact, we never met the Jess that run away from the encounter with Shotgun Jess in the restaurant, so that can be either the (future) Unamasked Jess or the Jess that killed Unmasked Jess.
- And there is of course always the possiblity that Killer Jess 2 is not the same person as Mean Jess, adding yet another layer to the events, entirely inexplicable within the movie.
After Our Jess returns to the ship at the end of the movie she becomes the killer-Jess who killed Downey + Salley with a knife.There's nothing to indicate the whole cycle is going to start from the beginning and we never learnt the origins of that particular Jess.