On the shelf in the living room is a picture of the real life Frank Gilbreth in uniform as an Army Major during WWI. This is visible outside the makeshift operating room during the mass tonsillectomies.
The big house the family moves to in Montclair is the same house set originally built for Judy Garland's family in Meet Me in St. Louis (1944). Fox didn't have an appropriate standing outdoor set so they rented time on the "St. Louis Street" on MGM lot #2.
The song "Sweet Lelani" that Tom Black is strumming with his ukulele on the beach was actually written by Harry Owens for his daughter in 1934, many years after the time that this movie is set. It also won an Academy Award for best song in 1937 when it appeared in the movie, Waikiki Wedding (1937).
The staircase/entrance way with the green wall paper and double doors under the landing to the left is the same staircase/entrance way used in the TV series Dark Shadows. The green wall paper is not there in Dark Shadows, but it's the exact same set.