It is mentioned that Grover's Corners is found at 42 degrees 40 minutes latitude and 70 degrees 37 minutes longitude. These coordinates are actually off the coast of Boston, Massachusetts in the Atlantic Ocean, not inland near the Massachusetts/New Hampshire border.
Emily keeps mentioning how bright the moon is and it is shown as a full moon. However, the establishing information date is June 7, 1901. On that date, the moon was in its last quarter and wouldn't even have been visible in the early evening.
The beginning of the movie takes place on June 7, 1901. That night everyone comments on how beautiful the moon is and we later learn it is 8:30pm. The moon did not rise until midnight on that date. In fact the sun did not set until 8:30pm. Additionally, crickets can be heard loudly chirping throughout these scenes. This would be very unusual for early June, but common in late August.