When Mary Kate interrupts the father fly fishing after storming off, the father says that he has been fishing for a particular wily salmon for ten years. Salmon almost always expire after returning to fresh water to spawn (at an age of four years or so) and a keen fisherman would know this.
Michaeleen introduces Sean to Mary Kate as from Pittsburgh, Massachusetts, USA. However, "Steel", "pig-iron furnaces", and "slag heaps" are more generally associated with Pittsburgh, Pennsylvania, USA. (Note: this is an obvious comedic device, showing that Michaeleen is not familiar with US geography.)
When Mary Kate and Sean drive to town in the buggy, the horn is on the left hand side of the bulkhead. When Mary Kate interrupts the father fly fishing after storming off, it has moved to the right side.
When Thornton and Danaher are at the Widow Tillane's bidding for the cottage, Danaher's highest bid is 710. But in the bar, the accordion player says he heard that Danaher bid up to 810 and nobody corrected him. It is possible that the bidding was longer when originally shot, and edited down, but they forgot to change the scene in the bar.
Towards the end of the movie when all the town folk are along the road waving at the car passing by, the car twice passes by the "IRA" member. He can be seen standing on the side of the road in his bright blue shirt.
When Sean steps off the train in Castletown he lays his sleeping bag down first and a suitcase down to the left of it. When Michaleen walks up to retrieve them the sleeping bag should be on his left and the suitcase on his right; instead they are reversed when he picks them up.
When Sean finds Mary Kate cleaning his cottage, you can see in the background that the bedroom door has been splintered with a large hole where the bolt would be. The door isn't splintered until later in the story, though, after Sean and Kate are married and he kicks the intact bedroom door down.
During the wedding reception when Will Danaher makes a toast to himself, the Widow Tillane can be seen in the background during the wide shot with her hands together holding a glass. During her close-up, her hands are apart, resting on the chair's arms.
Before Sean enters Mary Kate's home to ask her brother's permission to court her, the flowers he's carrying are very sad looking. After he enters the house, they change into a nice, full, colorful bouquet.
In the race meeting scene, two pipers are shown playing. The pipes they are playing are Scottish pipes characterized by having one bass and two tenor drones in addition to the chanter, traditional Irish pipes only have one bass and one tenor drone plus the chanter.
After Sean and Red's first confrontation in the pub, the publican is pulling a round of drinks for everyone, it can be seen that he is taking full pints from a line and pretending to fill them. In Ireland it is customary to have a row of drinks, such as Guniness, ready to be topped up as it is best served once it has settled.