Continuity mistake: In the beginning, after Ula gets his stitches done, he starts to put on his vest when he goes over and talks to Henry. The shot cuts to Henry and then back to Ula and then he starts to put it on again. (00:04:10)
Continuity mistake: Lucy's lemon wedge appears out of nowhere and disappears a couple of times before Henry even uses it. (00:11:45 - 00:13:20)
Continuity mistake: The waiter and Adam are talking about Lucy in the diner. There is a shot of Lucy across the diner. She is building a waffle house, and there is a glass of water to the left of her plate. Seconds later, the waitress walks by, and the glass is now a cup of coffee. (00:32:15)
Continuity mistake: When Drew is in her car at the restaurant, chastising Adam Sandler for faking not knowing how to read, a truck with the "Spam" logo drives by. The DVD commentary states the logo was added digitally later. When Adam's character runs back to his car, the logo is not on the truck anymore. (00:37:10 - 00:38:20)
Continuity mistake: When Lucy and Henry are talking on the parking lot (just after he pretended to be illiterate), a boat with purple sail appears out of nowhere behind Henry and then disappears. (00:37:45)
Continuity mistake: During the scene where Ula is in the tank as Drew and Sandler begin to make love, Ula's necklace starts out outside his shirt. As the scene ends and he leaves, the necklace winds up underneath his shirt. (01:08:00)
Continuity mistake: Throughout Henry's "song," Lucy keeps changing how she holds the cup. (01:09:00 - 01:10:30)
Continuity mistake: When Henry is leaving the dock, Alexa waves with her right hand. Notice the watch. When Alexa grabs some butt from Doug, The watch is now on left arm. (01:23:10)
Continuity mistake: The dark roots of Lucy's hair can be seen off and on throughout the movie. One day she will have dark roots, and the next day she won't.
Continuity mistake: Near the beginning of the movie, Ula was bitten by a shark and had massive stitches. Shortly after, when they are fixing the boat, all of the stitches are gone then a few minutes later they are back.
Continuity mistake: When Ula steps on Henry's pillow the dirt spot gets lighter from shot to shot. This occurs before Ula actually wipes the spot.
Continuity mistake: When Lucy watches the video tape for the first time, then goes outside and stands on the deck she turns to face Henry and her Dad. There are two small boats going toward each other just as they are about to pass the scene cuts back to Lucy, then you see the two about to pass each other again. This happens a total of three times.
Continuity mistake: When Lucy is telling Henry about her diary, her hair moves from behind her ear to covering her ear between shots.
Continuity mistake: Following their first encounter at the restaurant, Henry and Lucy are walking through the parking lot. The lighting conditions change from sunny to overcast between shots.
Continuity mistake: When Lucy has just painted the shed and comes into the house to watch the football game, her brother Doug is upside down in the chair doing crunches, then when Lucy sits on the couch in the next shot, her brother Doug is sitting up in the chair reading a magazine.
Chosen answer: Lucy's father previously told Henry that she only sings on days that she meets him - then you see a flash of her painting in the garage, singing a Beach Boys song. Right before he hands Henry the Beach Boys CD, he tells him that she's even singing again. Henry realized as he listened to CD - maybe if she is singing again, she is thinking of him, hence, remembering him. (It happens to be the same song that she was singing in the garage that's playing on the boat when Henry turns around to go back. It's called 'Wouldn't It Be Nice').
Why wouldn't the father just tell him directly "hey she's been painting and singing again, so she probably might remember you"