When Rachel is struggling with the anchor chain, the padlock changes position between shots. In one shot it dangles a few inches below her feet (which, by the way, would mean there's enough slack in the chain to escape). In another shot it's at her ankles, where it was fastened in the first place.
When walking on the boat bridge towards her son, on the close-ups, her hair falls backwards, like the wind is getting in her face. When the shot is changed to her right side, her hair is calm, and hanging down.
While talking to the "psychic" lady for the first time, Rachel holds the shoulder strap of her bag with her left hand. In the reflection in the window behind the lady her hand is down, however.
In all phone calls Rachel makes, the ringing sound of all the calls is a foreign long ring in equidistant intervals. This is used in many parts of the world and the particular 'note' of the sound is mainly an American tone. British phone ring-tones are sequences of two tone/pulses and therefore completely different. All the people Rachel calls are in Britain.
When Rachel first enters the town of Ingonish she walks past a sign stating the population. Scottish towns don't have these.
When Rachel see her son at the dock and he pulls her in the water. Between the shots of Thomas pulling her leg you see clearly see a grown man in a wig pulling her leg as well not showing his face.
When Rachel leaves the cottage for the first time to walk to the village along the beach, she walks along the beach to the right, indicating that the village is to the right of the cottage. She arrives in the village walking along the beach from the right, indicating that the village is to the left of the cottage.