Dill and Mary fall while running in the rain leaving her skirt muddy and soaked from her hip to her knee. In the very next scene at the door, the mud stain is gone and upon entering the room her clothes are completely dry.
As Crawford and Billie Burke exit the room after telling Gable Crawford's to be married, he takes out his cigarette case and opens it. The scene cuts to Butterworth coming in and back to Gable who suddenly doesn't have the case out and is leaning against a table.
When Dill and Mary are driving in the Rolls Royce, the camera pans up from the grill and the "Spirit of Ecstacy" hood ornament is not there. However, moments later when the camera view changes to the car interior, you can clearly see the ornament through the windshield.
When Mary shows Jeff a picture of the three of them as kids, it's a photo of children with the three star's adult pictures obviously pasted on their bodies - Mary even has on lipstick. Though they did at least use a picture of Gable without a mustache.