Why the movie doesn't work.

"I was not unhappy with the film at all but there are holes in it. The problem is it wasn't my story." - Neil Jordan

That the director is admitting not only that it's NOT HIS STORY but also to the fact that there are holes in the film means it doesn't work. That's what he's saying in the quote.

But, since I'm a sucker for talking about things that will never matter while on the internet, I'll continue.

Now, I enjoyed the movie to a point. Eventually it got sort of tiring and the end where she played house with Vivienne felt sort of dull and formulaic for such an atypical film. But I digress.

The whole "Claire is Vivienne" explanation simply isn't satisfying, because in order to make it work you have to throw out the entire movie. Without doing that, it doesn't work. I could drum up a lot of interesting interpretations of films if I were just to gleefully ignore the whole of the film's plot and chose to infer a subplot from the art design. Yes, there is a lot of suggestive imagery and the lines between dream and reality blur intentionally fairly often. As a film about psychic linking of two people, it very obviously plays with their identities (e.g. the haircut, the car scene, the typical Jordan androgyny). But the interpretation being suggested requires the entire narrative to be thrown out.

The thing of it is, if you're going to use an unreliable narrator (which this interpretation is implying Claire is) then you can't also show us a wealth of scenes from the point of view of OTHER characters (husband, doctor, police, etc). The film is NOT shown from only Claire's POV, as another thread suggested. There is also the intro scene explaining the flood, which is clearly meant for the audience and is not a delusion of Claire's. There's too much in the film that either doesn't support or directly contradicts the MPD explanation. When you have to throw out the whole movie to make your interpretations work, you no longer have a working interpretation.

You can't pick and choose like that. If you're saying that Claire is Vivienne then there has to actually be some event transpiring in order to make this the case. Otherwise no one is anyone, because nothing that we've just seen on screen is reliable and it doesn't mean anything at all.

There have been plenty of films and series where this thing has been done correctly and it actually stands up to review. This is not one of those cases. There two simple explanations as to why that is. Either:
1. as Jordan admits the film has holes and the story is not his the begin with so he attempted and failed to potray this MPD plot
or more likely,
2. because it isn't what was being portrayed in the first place, and you're reading far too much into the film. Even still, there are inconsistencies and holes about, but it's not nearly as problematic as the reaching MPD interpretation.