There is little doubt that this movie is very much open to interpretation. There are several possible explanations and in most cases plenty of viewers will love it even though they have no idea what happened. To be honest there can't be many people who completely understood the movie the first time they watched it unless they had some inside knowledge.
The real explanation follows "The Philosophy of Time Travel" and you can read it here. When you follow this explanation there doesn't seem to be any holes in the plot. Every scene makes sense, the story is consistent and the whole movie comes together.
Here are some of the alternative theories.
It is implied in the film that Donnie is a schizophrenic and therefore the film is him going through an episode of his illness. This theory is plausible because every single event could be put down to this. Hallucinations and hearing voices is a schizophrenic trait and could easily explain Frank’s appearance. There is a scene with Donnie’s therapist at the end of the film where she admits to giving Donnie placebo’s as medication for his illness. This would suggest that he in fact never was a schizophrenic. For me Richard Kelly put the idea of Donnie being schizophrenic into the movie deliberately as a red herring. It's an easier alternative theory that allows first time viewers to still enjoy the movie.
The whole movie was a dream theory is of course possible but ultimately pointless. When he goes to sleep on October 2nd at the beginning of the movie he dreams this mystical adventure just before he gets smooshed by jet engine.
The obvious hole in this theory is why do the first few minutes of October 2nd happen twice? An easy theory to enjoy maybe for the first watch but why would the director create this amazing magical alternative Universe theory and then just make it all out to be a dream?
This is quite a popular theory. It portrays Frank as a kind of Ghost of Christmas Future character who saves Donnie and then either shows him or allows him to live the next 28 days of his life. At the end Donnie returns back to October 2nd and now has the opportunity to choose his own fate.
So many bad things happened in those 28 days including his girlfriend getting killed and Donnie becoming a killer himself that he decides to stay in bed at the end of the film to sacrifice himself for the good of others. By dying he saves Frank, Gretchen and his mother and sister from a plane crash.
Unfortunately this theory asks more questions than it answers:
The biggest weakness in this theory is the fact that Donnie is shown or lives out a completely different future from what would normally have happened. Most of the events only happen because we are within a Tangent Universe.
None of these things would happen in the real world. What's the point in Donnie being shown an alternate future and then given the choice to live or die based on events that wont happen?
There are just too many plot flaws with this theory. It just doesn't work and there are virtually no scenes in the movie to back it up.
here is a theory out there that follows The Philosophy of Time Travel but with one major change. The idea is that every 28 days the Tangent Universe collapses, then loops back round to October 2nd and starts over again. Basically the Tangent Universe is a repeating time-loop that will continue until Donnie is successful in returning the jet engine into the Primary Universe. The film is Donnie's first successful attempt at returning the jet engine and there have been several failed attempts before.
I don't think this idea follows The Philosophy Of Time Travel accurately enough. The Tangent Universe only lasts for several weeks before it collapses and destroys the whole Universe. If it looped back round every time then the Universe wouldn't be in danger.
This theory seems to hinge on only a few pieces of the movie. The main basis of this theory is that Donnie wakes up on the mountain laughing at the beginning of the film. He's laughing as if he remembers something from the previous Tangent Universe loop.
Now the major flaw there is Donnie wakes up on the mountain on October 1st yet the Tangent Universe doesn't start until midnight on October 2nd. Why would time loop round to before the start of the Tangent Universe? Another thing is wouldn't you find it a little amusing if you woke up half way up a mountain. Surely that is a better explanation for him laughing.
Another huge flaw in this theory is if it was true the Universe would never be in any danger. Everytime Donnie failed the 28 days would just restart. This goes completely gainst the PoTT and makes the whole thing quite pointless.
Another point in this theory is the characters like Mrs Pomeroy, Grandma Death, Dr. Thurman all seem to have some kind of inside knowledge and a sense of what's going, like they have done this before. Well yes they do but not because they have done this several times before, it's because they are the Manipulated Living. There behaviour may be irrational or bizarre as they are trying to guide the Living Receiver to return the Artifact. They subconsciously behave in the necessary way in order for Donnie to succeed.