No one ever read any Poe?

All the people bitching about plot holes, you haven't read any Poe?

It's called an unreliable narrator.

Maybe it's more difficult to convey in film than in writing, but to me it seemed obvious this was what this was.

Yes, it's unrealistic that the funeral director could cause not one but two car accidents without being hurt or spotted, and that he could drug so many people with absolutely no one catching on.
Plus, he does speak to actual dead people. The pervert cop's brother was clearly dead, and he was still talking to him like he did Anna.
So how sane was this guy?

Paul had been hallucinating Anna for days before encountering the funeral director.
How sane was he?

How sane was Anna before her 'death'? Her pill popping, depressed mood, and extreme overreaction to thinking Paul was breaking up with her cast a lot of doubt on her mental state.

The viewer isn't supposed to know what's real and what isn't. There's "plot holes" for the idea that she was alive and the idea that she was dead, and I believe that was totally by design.