Darrin's father states that Michelangelo was 85 when he "built the Pauline Chapel." Michelangelo did not build the Pauline Chapel, but he did paint two frescoes for it from ages 67 to 74.
While the facts about Churchill and Verdi are correct, Michaelangelo painted the Sistine Chapel when he was 33-37 years old.
The train that Mrs. Stevens is on has a diesel locomotive, but when she pulls the cord they show the wheels of a stream locomotive braking.
When Phyllis pulls the train's emergency chord it's the wheels of a steam locomotive that screech to a halt not a diesel train which is the type of train she is traveling on.
The first time Phyllis pulls the emergency cord on the train, about nineteen minutes in, the car's inside wall which she is next to waves back and forth wildly. This shows that the set is constructed of light plywood instead of metal.