Factual error: The mansion Allie is staying in over the summer is Boone Hall Plantation in South Carolina, near Charleston. It was built in the 1930's, so factually the house couldn't have been in the family as long as the characters make it seem. A lot of the filming was also done in Kiawah, an island near Folly Beach.
Factual error: When Allie is looking at the moon before entering the house with Noah, there are a few contrails barely visible in the sky, but there couldn't have been any contrails back in those days because planes didn't fly that high or give off the same exhaust as modern-day planes. (00:29:10)
Factual error: Allie and Noah pass a small grocery store sign in window (Peaches 2 1/2 size 3/$1). That price is correct for about 1962, but not the time frame of early 1940s.
Factual error: When Allie goes back to see Noah and he asks her if she's hungry, he "catches" dinner. He picks up a crab net with about a half dozen blue crabs in it. Anyone who has ever crabbed, knows you have to pick the net up fast and keep pressure on the crabs or they will exit the net on the way up. Noah picks up the net so slow, there is no way he'd have caught any crabs in it. It is obviously filled with staged crabs.
Answer: She doesn't remember being married. Using her married name would only serve to confuse and upset her.