In his opening monologue, Jack jokingly claims that he left home two hours ago and walked all the way to the studio. At the time, Jack lived on Roxbury Drive in Beverly Hills, and he was filming his show at Universal Studios Hollywood. For the record, that studio is 9 miles away from his house, with the Hollywood Hills in between. Google Maps estimates that it would take 3 hours and 10 minutes to walk there. (And since Mr. Benny was 69 years old at the time, we can probably assume that it would take him even longer.)
During Jack's introductory conversation with singer Connie Francis in this 1963 episode, she says that she was born in 1940 (even though she was actually born in 1938). Jack quickly changes the subject, rather than reveal his own age. For the record, Jack Benny was born in 1894.
Connie's song "Follow the Boys" is from her 1963 movie of the same name.