The portrait hanging on the wall behind the judge in Margaret's dream is the same portrait hanging behind the judge in the actual court. It is the so-called Athenaeum Portrait of George Washington painted by Gilbert Stuart (1755-1828), which was begun, but never finished when Washington was 65 years old. It has since become iconic and is the basis of the representation of the 1st President of the U.S. that appears on the $1 bill.
The Anderson's family car is shown in this episode: a 1957 Ford Galaxie. It is noteworthy that Betty is the driver, not Margaret. Margaret does not learn to drive until later in the season: Margaret Learns to Drive (1957).