The papers had the date of the 16th which they say is the next day but when handing over the film the desk diary says the 10th.
The newspapers contain a story on the front age proclaiming that a Yankees pitcher won his 20th game. The newspapers are dated in mid-July. No pitcher in the modern era has ever won his 20th game in July, and the wins leader on the Yankees in 1947 was Allie Reynolds who won a total of 19 games that year.
The pen and set of keys that float above Peggy's desk don't cast shadows.
Jarvis gives Howard a Bloody Mary with a stalk of celery in it. Howard is subsequently seen munching on the celery, which is completely clean. It should have visible residue from the beverage on it.
When Agent Carter is searching Dr. Wilkes' home and finds the airplane boarding passes under the floorboards, the airplane silhouettes on the pass are those of a modern day jet airliner which did not exist in 1947.
The time period for this is the year 1947. When Peggy looks at the airline ticket jacket the artwork on it depicts a Boeing 707. This passenger jetliner didn't go into service until October 1958 with Pan Am airlines.
In several scenes set in Howard Stark's Basement, a green and red CASTROL motor oil advertising sign can be seen in the background. This particular logo was not used by Castrol until the late 60's or early 70's.
When Agent Carter, Howard Stark and Dr. Wilkes are talking at Stark's lab, the Castrol logo visible on the wall wasn't introduced until 1999.
The chairs seen in the Arena Club's secret meeting room are of a style not available in 1947. They sport 5-point bases and tilt-tension adjustment knobs and pneumatic lift handles on the underside of the seats. 5-point bases weren't introduced until the 1950s and didn't become widespread until the 1980s, with the then-standard 4-point bases being fully phased out in the early 1990s. Tilt-tension adjustment and pneumatic lift controls weren't added as features on chairs until the 1970s.