The opening sequence begins with the screen caption "Benedict Canyon, Los Angeles, 1961". When Cary Grant's car is shown, it is a Rolls-Royce Silver Shadow, which didn't begin production until 1965, and it appears to be a UK model from around 1975. A better car to show would have been a Silver Cloud II with left-hand drive.
Dyan Cannon arrives at Cary Grant's house driving a red Mustang convertible, a car whose first model year was "1964½" (sic). Based on some dates given earlier, this segment is sometime in 1961. In the next episode, in an exchange with Mrs. Alfred Hitchcock, it is confirmed that Cary is still married to Betsy Drake (and will be until sometime in 1962). Either of these dates are well before the Mustang came out.
In 1962, Cary Grant is seen using a touch-tone telephone in his house. Touch-tone phones were not introduced until Nov. 18, 1963, and only in limited areas (Pittsburgh PA).