The portrait hanging along the staircase of the beach cottage is of Captain Daniel Gregg, played by Rex Harrison, from The Ghost and Mrs. Muir (1947).
Shortly after the family arrives at the beach house, James Stewart starts to climb the stairway and the newel post top comes off in his hand. This appears to be a tribute to the same thing happening to him in It's a Wonderful Life (1946).
The statue of the woman's head on the Hobbs' bedroom mantelpiece can also be seen in Harvey (1950), also starring James Stewart and Minerva Urecal.
First of two films in which Fabian plays the boyfriend to James Stewart's on-screen daughter, the second being Dear Brigitte (1965).