(written from a Production point of view)
According to the script of TNG: "Too Short a Season",  the USS Falcon was the first ship on which Captain Mark Jameson was the commanding officer. Commander William T. Riker's father, Kyle Riker, served under Jameson. By 2364, this ship was renowned for its missions and the Mordan IV rescue. The scene in which the Falcon was mentioned did not make it to the final episode.