Captain Gregg appears next to Lucy on the train and scoffs at Fairley's motivations. The scenery going past on Gregg's side of the car is full of buildings and billboards, right up close to the train tracks. When the focus is on Lucy, the scenery consists of open fields, trees in the distance, and farmland. This goes back and forth several times throughout the scene.
Anna Muir's name is carved into a post on the shore when she is a young girl. Over time, the post and breaker severely deteriorate due to wind, waves, and time. However, the letters carved into the wood post remain fresh and legible as if they had just been carved.
Before the last scene, Martha puts a glass of milk on the table next to a now-old Mrs. Muir. Martha leaves the bedroom and seemingly closes the door behind her. In the next shot of Mrs. Muir, the door is wide open.
When Fairley takes the cab ride with Mrs. Muir, the raindrops on his hat change noticeably from shot to shot.
(at around 1h 15 mins) A horse, who moments prior, was facing the left, eating grass, is now facing right with its tail up, and manure can be faintly seen excreted from its rear, in perspective of Mrs. Muir's right shoulder. This happens after the ghost says "But be careful, there may be breakers ahead" and Mrs. Muir responds "I will, Daniel" and departs on the unpaved road.
Although Captain Gregg promised never to speak with Anna, he clearly breaks his word. Evidence of this can be seen as he throws the in-laws out of the house: Anna can be seen in the foreground watching without fear or confusion, thus revealing that she is aware of his presence and not scared of him.
As Lucy and Captain Gregg exit the house after her death, Captain Gregg's shoe catches on the rug and his shadow passes over her body. Both of these would seen to indicate a corporeal body. But not in this film. In this film the producers decided to forego special effects. As such, this film stays true to its own definition of what a ghost is.
Although Capt. Gregg states early in the movie that he is a spirit and has no physical body, he does a very good job of casting shadows on walls, doors, etc.
As Mrs. Muir's sister-in-law and mother-in-law come down the stairs towards the ghost of Capt. Gregg, the mother-in-law has to squeeze around Rex Harrison's body to finish descending the staircase, right before he grabs the elbows of the two ladies.
Early in the movie Mrs. Muir walks down the stairs of the house with a lit candle that casts a shadow of the whole candlestick on the walls.
The movie opens at the turn of the century when Anna is about 6-8 years old. About 10 or so years later, when she comes home from college, everyone is dressed as if it were the 1940s.
At the beach, a man carves Anna Muir's name into a post buried in the shore and much is made of the fact that every ship passing by will see it forever, but the side of the post he carves her name in faces inland, meaning no one on a passing ship will ever see it. The name wasn't carved into both sides, either - Anna's mother, Mrs. Muir, has to walk around to the inland side to see it.
When Lucy is talking with her sister-in-law, Eva, and her mother-in-law in her room, Eva is facing Lucy and the telescope is right behind Lucy. Captain Gregg moves behind Lucy to the telescope and then moves the telescope, rotating it 90 degrees. Eva should have noticed that the telescope turned all by itself, since Captain Gregg was not visible to them, but she doesn't react to anything.
(At around 39 minutes) As Mrs. Muir's mother-in-law is speaking to her, the shadow of a boom mic is visible in the corner.