The date on a letter Kitty is seen typing for Wyn in a fully-staffed office was a Sunday, not a workday.
When Kitty and Wyn are in a speakeasy, the 1932 election returns are being broadcast over the radio. The announcer says that FDR has won Pennsylvania; Hoover won Pennsylvania in the election.
No company, even in the early 19th century, would locate a burglar alarm button immediately so close to another button for a non-emergency task. The likelihood of error is too great, especially when one button calls a minimum-wage stock boy and the other summons the police.
When Tom Foyle's waste basket catches fire, Kitty pours whiskey on it to put it out, yet the fire doesn't flare up. However, bottled whiskey is usually less than 50% alcohol (100 proof) and will not readily burn, let alone flare. It takes a much higher concentration of alcohol (e.g., Bacardi 151 rum or pure ethanol) to burn steadily.
It has been stated that "A doctor would not be automatically dispatched on a burglar alarm" and that this was a goof. The doctor responded because a second lady fainted after yelling out "My blood pressure" during the alarm, followed by the hair salon worker calling for a doctor.
At the beginning, the film is set in the year 1900. However, the song being played, "I Want a Girl", wasn't written until 1911.
During Kitty's first date with Wyn, when she is wondering why he took her up to NYC instead of somewhere in Philadelphia, she tells him the story about "when I was going to high school in Manatu, Illinois, if a fella wanted to take a girl out and he didn't particularly care about being seen with her, he always took her up to Chicago". Just a few minutes earlier in the film, they show Kitty at 15 years old (high school age) and going out to see the socialites attend the Philadelphia Assembly. The voiceover narration also states early in the film that Grisgom Street in Philadelphia is where "pop brought her up".
As an add to the other character error, in the book "Kitty Foyle" that the film is based on, Kitty does indeed go to High School in Manatu, Illinois. Presumably, when the film was released enough people would have read the book to get the reference.