There are film critics who, whenever they review a movie about time travel, rehearse the antinomies of retrocausation. This was a weakness of Roger Ebert. But that's a mistake. We need to be more discriminating when it comes to the genre.
i) Time travel that doesn't change the past is coherent. Likewise, if a person traveled into the future and stayed there, that would be coherent.
But changing the past is incoherent. By the same token, traveling into the future, then returning to the present, creates the same problems. Even if the traveler didn't intend to change his own time, by returning to the present with advance knowledge, that will affect his actions in many subtle ways. He behaves differently than before he took that trip. His very presence changes the status quo, because his present-day actions are now informed by foreknowledge.
Problem is, the impossible time-travel scenarios are the very scenarios we most enjoy. So we have a choice: would you rather have time travel stories or not have time travel stories? If you enjoy the genre, then stop bitching about the antinomies. That's the price you pay for the genre.
If a character was simply a detached observer, then time travel would be coherent. But we prefer stories in which the character interacts with his environment. That's because the character is a stand-in for the reader or viewer. He vicariously takes us to times and places where we'd like to go. We experience it through his eyes, ears, and feet.
That goes to the limitations as well as the distinctive appeal of the genre. Can't have one without the other.
ii) This is part of the willing suspension of belief. We do that all the time with movies we watch. Why be so picky about time travel films?
We don't demand that stories be realistic. We like unrealistic stories. The imagination can take us places where we can't go in real life. That's what makes it appealing.
iii) Given the genre, just about every film about time travel will suffer from this paradox. Unless you hate the genre, there's no point attacking every example of the genre. For that "flaw" will be present in just about every specimen. It can't be eliminated without eliminating the genre. So we should discriminate between good examples and bad examples of the genre.
That doesn't mean time travel stories are above criticism. That doesn't mean they are equally good. It depends on how well or badly the theme is handled.
iv) In general, I think it works best if the story takes the possibility of time travel for granted, without explaining it. Just like an author doesn't stop to detail the metaphysical machinery of magic when he tells a story about wizards. Rather, that's just a given. If you can't accept that on its own terms, read a different kind of story. Same thing with fire-breathing dragons. We really don't want a biological theory.
I've seen movies that make the mistake of offering a scientific explanation for vampires. But it's more plausible when they are viewed as occult creatures.
v) There are philosophers and physicists who labor to elude the antinomies of time travel. If a director or screenwriter offers a philosophically serious explanation, I think we should give him credit, even if theory can't withstand scrutiny. I'd cut him some slack. At least he respected the intelligence of the audience.
However, even that can be a problem. For instance, there's a scene in Minority Report where a character "resolves" the dilemma with an object lesson:
Anderton picks up a wooden ball and rolls it toward Witwer, who catches it before it lands on the ground. When asked why he caught the ball, Witwer says "Because it was going to fall." Anderton replies, "But it didn't." Then confidently tells him, "The fact that you prevented it from happening doesn't change the fact that it was going to happen."
But the problem with that illustration is that it freezes the attention of the audience. A thoughtful viewer will keep pondering the validity of the illustration long after that scene. He's mentally stuck on that scene. The story continues, but his mind is back on that scene. So it's distracting.
A good director doesn't want the audience to keep thinking about that scene, to keep puzzling over that illustration. He wants the plot to move forward, and the viewer to move in tandem.
vi) Where directors come in for deserved criticism is when the film gives a half-baked explanation for time travel. I've never understood the mentality of SF directors who spend hundreds of millions of dollars on a film, but can't budget for a decent screenwriter.
Sometimes they come up with a "scientific" theory of time travel that's pure poppycock. It's just a lazy, throwaway explanation. No attempt to be scientifically or philosophically plausible.
Plot holes and continuity errors are often due to slipshod writing. The director or screenwriter made no effort to be consistent. They take no pride in craftsmanship. It's just about making a quick buck. Another forgettable film.
vii) But in an open-ended TV series or movie franchise, plot holes and continuity problems may be due to the fact that the director or screenwriter didn't or couldn't think that far ahead. They had no idea the film would be a blockbuster, so they didn't plan for a sequel. They don't know how many seasons the series will run for, so they can't anticipate where the story will go. Plot holes and continuity errors that happen for that reason are more excusable.
In a movie or miniseries, that's avoidable because it's all written ahead of time. However, improvisation can have its own benefits, even if it generates inconcinnities.
For instance, Chris Carter did a lot of improvising in The X-Files. Sometimes it works and sometimes it doesn't. But he had lots of interesting ideas, so the creative momentum of one unforeseen development sparking another opened up many good fresh storylines. He didn't know where-all he was headed when he began, but in the right hands, that's an artistic stimulus.
In addition, discontinuity errors can be deliberate. A new director or screenwriter may think the original idea was bad to begin with, so he scraps it and strikes out in a new direction. Or maybe he thought the original idea was good, but exhausted its dramatic potential.