Continuity mistake: Danny and Linda are hugging after Danny tells the boys to go pay your respects to the WWII Memorial. In the next shot they are standing apart as when he told them to go pay their respects to the memorial. (00:54:34)
Continuity mistake: Near The End of the episode, just after Danny's family is looking at the Statue of Liberty, Danny puts his arm around Linda, and then does it a second time.
Answer: It is an NYPD Detective Bureau lapel pin. If you zoom in on a pic of "Danny Reagan," you will see that the pin has the letters DB on it.