The Tragedy at Marsdon Manor - S3-E6
Plot hole: The murderer is in possession of chloroform from the doctor's cabinet, but there's no realistic timeframe when they could have done it, nor any explanation why the doctor notices it completely at random when Poirot visits, just approaching the medicine cabinet, something he routinely opens and looks through during the day.
The Tragedy at Marsdon Manor - S3-E6
Plot hole: The murderer planned everything making it seems accidental. They perfectly managed to fool the coroner and need only to be alone at the mansion to get rid of the murder weapon. So what they do is...they go through great risks to make everyone know someone tried to murder the wife too, making it obvious that there is a killer at large, which only makes the investigation more stringent and most importantly, keeps the police on the premises for surveillance preventing them from disposing of the weapon (like almost everything in this episode's plot it is not a flaw of the original story, but of the dramatization, who added practically every minor character).
The Tragedy at Marsdon Manor - S3-E6
Plot hole: It is revealed towards the end of the episode that the painting Mrs. Maltravers did when the murder took place was not painted that day and that time of the day, because it had the wrong shadows. But we actually saw what was on the canvas when the secretary was leaving to go to the bank, and it was that exact painting in an early state. She also came up with the idea for the murder the night before, making even more unbelievable that she'd just have the alibi painting ready and waiting the morning after. That without mentioning the fact that the murder itself as described is not something that would have required an amount of time needed to make a whole painting, and that she could have finished it later anyway (she gave it to Hastings a day later, after all).