The Secret of the Flame Tree - S6-E2
Stupidity: Sylvie Baptiste is a successful writer, and she published novels after her masterpiece. The idea that she'd lose all her fame and fortune if someone published an academic paper making a completely unsubstantiated claim (if Sylvie does not have an original manuscript of the novel, neither does Lizzie) about her novel being the work of her crazy sister, is simply absurd. A good copyright lawyer or even any decent PR agency would put the appropriate spin to the accusations easily, and since her sister is certainly not gonna sue her and Sylvie is her only possible tutor, all those people supposedly very well connected with the academia and industry and shrewd in marketing their work, overreact for nothing. Even better; Humphrey has not even exposed the killer (or that it is a murder at all), and the university announces already that they plan to give a posthumous PhD to the deceased, for the paper she hasn't finished, based on an accusation with no evidence.
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.
Answer: Most likely they had only tropical exotic drinks, he wanted an old fashioned English beer.