The 'photograph' on the shelf
Unless I missed something, didn't the current owner of the house keep looking at a photograph taken of Betsy and her teacher?
If the story was set in 1817, the first photograph is documented in 1827, a full decade after this story. And even then, it wasn't until around the Civil War the photograph really began to be used to everyday people.
I only watched this movie because I saw Sissy Spacek and Donald Sutherland were in the cast; I am suprised those two intelligent people didn't catch this (let alone whoever was supposed to be the researcher).