Because this is a Roscoe-centric episode, Louis Quinn gets first billing in the end credits. Additionally, his real-life wife, Christine Nelson, plays his romantic interest; this was the last of her four guest appearances on the series.
Roscoe is the only original-series regular whose last name was never given. However, in this episode, most of the (non-regular) characters address him as "Mr. Roscoe," which might lead one to suspect that it's actually his last name.
The voice on the radio announcing the race results is Roger Smith.
The cop assisting Jeff is played by Richard X. Slattery; at one point, we're told that Lt. Gilmore is on vacation. Presumably Byron Keith was unavailable that week, possibly due to illness. A couple of months later, Slattery returned in another Gilmore-less episode, "The Gemmologist Caper."
The name on the mailbox at his apartment house merely states Roscoe, giving credence that is his last name.