August says Jacob is an Ivy League grad. Although the term "Ivy Colleges" was used in the early 1930s, "Ivy League" was first used in the Christian Science Monitor on February 7, 1935. The "Ivy League" wasn't officially established until 1954.
The blueish-grayish tights Reese Witherspoon wears are clearly made of a fabric containing nylon. Natural fibers (cotton, wool, silk...) would not result in the even, semi-opaque aspect with no wrinkles in the knee and foot area.
Nylon was not invented before the late 30ies, so the tights are an anachronism.
The night Jacob and Marlena run away, when Marlena rushes in Jacob's compartment, she wears a black satin robe over her dress which can also be seen when they are standing over the edge of the train ready to jump. However, when they jump and start walking away from the trails, Marlena wears only her dress. The satin robe reappears when they get in the hotel room.
When Marlena first appears with her horses and Silver Star before the performance, the horses wear halters. However, in the circus ring when she is working them at liberty, they don't have halters on. Cut to Marlena as she takes her bow, the line of horses rear behind her and all have on halters again.
After their first dinner together, August is very drunk and Marlena carries him in their bedroom. When she comes out again, where Jacob is sitting, she pulls the drapes together, but doesn't close them completely - there is a significant gap between them. However, when Jacob leaves after Marlena has asked him to, the drapes are completely closed.
The goof item below may give away important plot points.
Incorrectly regarded as goofs
When Jacob is going to stab August in the bedroom Marlena has a black left eye. The next morning when she comes to visit Jacob the black eye is gone.
Actually, it's not a black eye. It's her make-ups that is blurred.