Ken mentions that the Warner Brothers logo they show is the current logo, not the 1961 logo:
So is it?
IMDb says so:
The truth is a little more convoluted. Here's a brief history of the WB logo:
Here's the logo that WB used for the 1954 film Dial M For Murder:
It seems possible that a limo driver in 1961 would have a sign that looked like the one in the film.