A couple of late suggestions for the original query.
50a: I concluded that 'eye' represented 'discrimination' in the way that someone with discrimination may be said to have an 'eye' for the subject in question. I might have got this wrong though.
24d: This was a real puzzle but I've finally come to the view that it's a humorous one, playing on words such as democratic, autocratic, etc. to suggest that a hippocratic person would be one who likes to wallow in power. (-cracy/-cratic being based on the Greek word for 'power'). So, the clue is saying that this is a pledge made by an MD and not, as it may sound, by a power-loving hippo!