Factual error: In the beginning of the film, when Nick flashes back to 1922, he mentions that the buildings were taller, and a shot of the Empire State Building is shown. But construction on that didn't even start until 1931. Even the Chrysler Building didn't start construction until 1929.
Other mistake: At the very end Nick writes "The Great" in ink above the typed title "Gatsby" on the cover of his manuscript. The E in "The" is a completely different style to the E in "Great."
Suggested correction: It is the therapist who writes The Great. As for why the Es look different, not everyone one is able to write their letters the same every single time.