When DeDe walks into Joe's apartment at the end of their date, she places her handbag on the floor a few steps across from the door. When she comes back in to get the bag because she forgot it after she leaves, she reaches for the bag just inside the door.
When Joe enters the factory turnstile (view from the back), the man next in line is not the same man behind him when Joe gets hit by the turnstile (view from the front). This might be deliberate on the part of the film makers. When he walks through the parking lot, most of the people around him are dressed as blue-collar workers (open collars and jackets). When he enters the gate, most of the people behind him are white collar workers (jacket and tie under overcoat).
In the morning when the daisy gets stepped on, everyone's shadows are to their right. Later that afternoon, when Joe fixes the daisy, his shadow is also to his right, and from the same camera angle. In the afternoon Joe's shadow would have been of a different angle.
Mr. Graynamore sets out the credit cards atop Joe's stereo, orientating them so Joe can read them. Joe takes one and turns it over as if it were turned upside down.
Joe's trunks change their positions depending on what the activity Joe is doing, while they are in the ocean.
The first night on the ship, when they are having dinner, we see a crescent moon with horns pointing downward. The crescent moon is actually a spherical object that is illuminated by the light of the sun. Therefore, the "horns" of the crescent always point away from the sun. In the northern hemisphere of the Earth, when the evening sun is below the horizon in the west, the horns of the crescent moon point upward and to the left. And several weeks later, when the morning sun is below the horizon in the east, the horns point upward and to the right. Downward horns would imply that the sun is above the horizon, therefore it would not be night.
The Medical League Building - Long Island City Branch has a street address of 941. Addresses in Long Island City, Queens are hyphenated, such as 25-81.
When Joe is golfing on the raft, the wind blows his putting green up and over. Patricia can be seen lifting her hand ostensibly to protect herself. However, she is supposed to be unconscious.
When Joe sits on the beach all night and the sun rises in the morning, the light casts onto Joe from the bottom up, rather than the top down as would be expected naturally.
In the storm scene, Joe and Patricia are facing each other (having just kissed) when the boom hits Patricia in the back of the head. In the subsequent cut, she is flung (face-first) into the ocean, but Joe is nowhere to be seen - she would have taken him with her, or at least knocked him over. He's also taller than she is, so he would have been hit too (clearly, nobody had time to duck).
When Joe catches the hammerhead shark it is clearly a stuffed mock up. One can see the folds in the fabric.
When Joe goes to the doctor and is standing at the fireplace there is a stain on his shirt, his right side then after there is no stain.
The credits say "Tom Hank's Make-Up Artist". That should be either "Tom Hanks' Make-Up Artist" or "Tom Hanks's Make-Up Artist".