Why didn't the Redferns sign the guest book? They didn't know at that point that Poirot would be there. If someone else had investigated the crime they wouldn't know to compare Patrick Redfern's signature with Felix Ruber's. They wouldn't know about the death of Alice Ruber.
shareI assume Redfern was just always careful not to leave his signature anywhere as he had used it to commit fraud
shareMrs Redfern was going to but got distracted. I thought it was just a plot device so that later it would be more dramatic when Poirot compares the cheque signature to the other signature in front of everybody and catches out Redfern that way.
Bye the way, did anyone else notice the other names in the guest book? Ivor Novello, Fred and Adele Astaire, Cole Porter, Charlie Chaplin, Maurice Chevalier and Marlene Dietrich - quite the who's who of guests!!