The Secret of the Flame Tree - S6-E2
Stupidity: The whole plot hinges on the fact that Goodman trusts 100% without any doubt ever the time of death (even if it would have been easy for the killer to change the time on the watch, one of the most common tricks used in murder mysteries), and that out of over 100 people nobody mentioned that one of the suspects was nowhere to be seen at the time in question, especially with the police asking specifically for that sort of hole in alibis. Also, the stage is tiny and the show happened literally in the middle of the day; during a slideshow projection it's practically impossible that everyone's eyes would be focused on the screen to the point of not noticing the movement from the tent.