Dickie's rings
I had another thread on this board about why Tom killed Peter and there were some great replies. But now late 2014 is the cutoff for threads (this board is happenin'!) Anyway, there's other threads now that succinctly deal with that issue, so I'll bring up the other major question I now have.
Why DOES Tom have Dickie's rings. Obviously it's because Tom loved Dickie and admired the rings; but he never really makes any explanation to Marge other than that Dickie is a liar. When Mr. Greanleaf says, "because there's only one explanation to be drawn," both Tom and the audience take that to mean that Tom has been found out and is about to be exposed. But, since that doesn't happen, what exactly do Mr. Greanleaf and the detective think that explanation is exactly? Clearly from that point on, Marge knows Tom did it.
At least there will be plenty implied.