Louis Lester is shown as a Black musician leading a racially mixed band. Though Black musicians were sometimes featured as special guests with white bands in the 1930's (Coleman Hawkins with Jack Hylton and Teddy Wilson and Lionel Hampton with Benny Goodman), racially mixed bands didn't become common until the 1950's.
The show identifies Prince George as the Prince of Wales. He was not; his older brother Edward was. Edward was next in line for the throne after George V died but abdicated to marry the woman he loved, American divorcée Wallis Simpson, so George VI became King without ever having been Prince of Wales.