In an unusual connection for the time (or possibly a product placement), the W&J Sloan Company in Beverly Hills - where Cheryl worked - was a real furniture and interior decorating firm founded in New York City in 1843. It went bankrupt in 1985. According to the end credits, the company supplied set decorations and furnishings for the film.
Cheryl's unusual little sports car is a 1953 Hillman Minx Mark VI convertible coupe. Original MSRP was $1,899 (about $18,300 in 2017). At auction in 2017, in excellent condition, it could fetch around $15,000. It's not very popular due to its small 77 cubic inch (1.3L) engine producing only 38 hp. It's main attraction was its high gas mileage - for the time - and not its 68 mph top speed, or that it took a whopping 36 seconds to go from 0-60 mph. The Mark VI was made only in the 1953 model year.
One of the newspapers that Cheryl Draper reads contains a story with the headline "Mercury New X-ray Source, Two Scientists Report". This same story appears in many movies and TV shows with newspaper close-up scenes. In real life it originally appeared in newspapers in 1934.
About 1:10 into the film, Cheryl drives by the brightly lit facade of the Four Star Theatre on Wilshire Blvd., where Julius Caesar (1953), starring Marlon Brando, was enjoying its exclusive Los Angeles premiere engagement.