Plot hole: The hole in the hat was pre-existing and the bullet was fired in advance and dropped. Poirot notices immediately the hole when Nick puts the hat down but somehow missed it while she was wearing it as she supported him. He also does not notice that the bullet has not been fired at that time - which would have been still hot if just fired, not at all if dropped. Most importantly, in the spot where they were sitting, it's not even possible to think where a shooter could have ever been hidden; nobody wonders where the mysterious shooter could have been or cares to investigate the circumstance despite knowing the very moment the supposed shot happened. The fact is basically ignored throughout the rest of the episode.
Plot hole: The whole premise of the plot is that nobody is staying at End House but Nick (and the servants); she even says explicitly that there is just one room that is usable and everyone else stays at the Majestic. During the party though, Freddie tells Maggie to go get her coat which is "in my room." They are at End House, not the hotel, how would Maggie have a room there? (00:35:00)
Plot hole: The killer's plan needs to have Maggie at End House - but it's achieved through Poirot's proposal to have Nick call her to act as added protection. But this makes no sense; Maggie's presence would have not protected Nick in any of the alleged attempts to her life; the frame would have crushed her too, she would have died in the car, she couldn't have prevented the rock from falling, and Nick was shot while the most famous detective was with her, even! A random little girl from Yorkshire would have not mattered, so it makes no sense that Poirot endangered someone for no gain.
