What are the trifles that the men ignore and the two women notice, and why does this happen?

Some of the "trifles" that the men miss are the arrangement of things in the kitchen, such as the breadbasket.  The emptiness of the bird cage is another "small" thing that the men in the play, the detectives, actually discard.  The cross stitching pattern that was disjointed and crooked, reflecting a sense of fear and a broken notion of attention span, was something that was dismissed.  Additionally, the sewing box, and not paying attention to it, was a minor detail that the men discarded.  These are but a few.  The largest "dismissive trifle" is, of course, the women's conversation.  The men see the women's discussion as gossip, or idle chatter.  They feel that the women's discussion of small or "trivial" matters could in no way lead to a discovery about the murder.  Part of this is myopic vision as both men and detectives.  As men, they feel that women focus on small and mindless matters, contributing to a traditionally narrow focus of women.  This is myopia that also reflects a sense of blindness as detectives.  The women talk about the crime!  They discuss the relationship between the husband and wife, the friction, the problems with both of them and the circumstances that might have led to the murder.  The women also talk about the murder itself, and retrace the steps of how the murder could have happened.  They do this through conversation and discussion.  This is what detectives are supposed to do:  Re-imagine the crime scene and hypothesize as to what could have transpired.  The women do this through conversation and discussion and in doing so, their "trifles" result in a greater detective analysis than the supposed male experts.