On the much debated topic of the hat -- given LE doesn't know the identity of BG, to me it would seem absolutely irresponsible to issue a sketch months after the fact with descriptive detail including exactly the hat he wore on Feb 13th. Much like clothing, who can say if the hat he wore on that particular day would've been recognizable from his general attire both before and after?
That's the reason LE suggests to focus on the face and forget the hat. If the murder was in any way planned, BG would be pretty stupid to wear distinctly identifiable clothing, including a hat, given it occured in a place where'd others might've obsevered his entry or departure.
The hat is meaningless, other than it obviously covered his hair -- otherwise it's significance would be much like LE asking for tips months later on someone wearing a green shirt. JMO