Are there times when we know more than Inspector Luton does? More than Jennifer? Or are we all, characters and readers, held with hints and suspicions until the end?

Yes, sometimes Jennifer's memories flirt with the truth, as though she's unconsciously skirting issues that scare her (because she's afraid there's more to her bits and pieces of memories than she's allowing herself to think), but once you've finished the book it's easy to see the clues planted throughout the book. While Jennifer's relating some of her experiences the reader gets a bit of foreshadow as to the ending, thus we know more than she consciously knows.

Yes we do know more than the inspector. This is one of the few, if not the only book, where I found the character of the inspector, offensive. While I realize that the author needed to solve the crime, I found that the way she did heavy handed.

Throughout the book we know more than Jennifer but the progression of her Alzheimer's makes this more evident. I think that she tried to supress some of the thoughts surrounding the death of her friend, and some of the flashbacks were certainly NOT in keeping with the progression of the disease and by that fact alone, we know more than she.
I agree with Janen, about the inspector and thought that she was heavy handed. I think the author tried to make her empathetic, but I felt she was too cold and heartless.