This is the first episode where Castle calls Beckett by her first name, Kate.
When Beckett discovers the bags of drugs hidden in the bus-station locker, she cuts one open and tastes a bit of it to identify it as heroin. Although this is a very common thing for cops to do in TV shows and movies, it is strictly against actual police procedure. Aside from rules against law-enforcement officers ingesting any illegal drugs, there is also the chance that an unknown powder found during an investigation might be laced with an even more dangerous or lethal poison (anthrax, ricin, and cyanide all also have white-powder forms).
This is the first time Beckett admits she enjoys having Castle around at the precinct. Up to now, she's only been disdainfully tolerant of his presence.
The Westies are not an organization with a long lineage. They were a small group in the 70's that worked with the Gambino family as enforcers and thugs. There are no longer any "Westies" as the group was broken up and most imprisoned or dead. Even the Mickey Spillane era of Irish centric criminal activity was not the "Westies". Most of the actual members were not from Ireland and were American born.
The knife Beckett uses to cut open the heroin package is a Kershaw Scallion.