Fun Fact: Originally Q was going to be behind the events of this episode.
I'm sorry Jeyl, don't trap me in a time loop.
This is an episode that just about gets by on a great atmosphere, there's something very unnerving about the ill and mumbling future Picard, that actually increases as he gets more coherent over the course of the show.
But yes, you think about it even slightly and the whole thing falls apart badly. I think, as is often the case with time twisty nut shows like this, the Trek need to try and explain what happened works against the mystery and intentional confusion of the episode because frankly there is no rational two paragraph explanation for what happened that won't make your eyes bleed (and of course, loosing the originally planned Q ending- has anyone mentioned that?- doesn't help the slightly desperate wrap up).
As an episode of a Twilight Zone style series that's more interested in posing questions and giving answers that could end with a wry raised "What reaaaaaally happened?" eyebrow this would probably work much better, as an episode of Star Trek it flounders.
Plus, and this is cruel nit picking, there are some shots where the double for Patrick Stewart laying on the bed is really unconvincing. Almost as if they got a completely bald guy and stapled some grey carpet round the sides of his head to replicate what hair Stewart had.