Factual error: At Tiffany's, just before Andrew proposes, Melanie says Christmas is "four months away," making it August. She immediately heads down to Alabama to finalize the divorce and tell her parents she's engaged, but she and the townspeople are wearing warm clothes, including a long-sleeved black turtleneck and tall boots for her, and mid-weight jackets for the guys. They'd die of heat stroke wearing those articles in August in Alabama.
Factual error: If Melanie is still married to her first husband when she is about to wed her New York man, than she would not have been able to obtain a marriage license, as it would have shown up that she is already married when they applied for a license. Therefore, Mr. Buford would not have been running into the wedding to inform her she was still married to Jake. She should have already known.
Factual error: While it may be an artistic thing for the movie, fulgerite (lighting + sand) does not create anything near as ornate, long, crystal clear or tentacle like as portrayed in the movie. If anything it leaves tubular or clump like structures that are more reminiscent of kitty litter.
Factual error: Melanie is walking up the aisle at her wedding in Alabama and her lawyer comes to tell her that she hasn't signed the divorce papers. The impression is given that she will sign them and then she can get married straight away. Alabama law states that you must wait 60 days following divorce before you can remarry. Melanie wouldn't have been able to get married even if she had signed the papers.