Joseph dumps Shannon into a filled bathtub fully clothed. She climbs out and heads for the door, but when she steps out into the hallway her clothing is dry.
During the land race scene, Joseph is carrying his flag on the back of his horse. The flag disappears and reappears between shots.
Shannon falls off her horse into the muddy water, submerged nearly to her neck. The next time we see her on her horse, her white shirt is dry and pristine.
When Shannon and Joseph first go to meet the ward boss, Shannon's face is splattered with blood, and she wipes some of it away. Later in the scene, the blood is back on her face.
When Joseph brings Shannon to her family after she gets shot, she is seen lying on the couch facing left. The next time we see her, she is facing right.
When the land race begins there are photographers taking pictures. They fire off flash powder. There would be no point doing that in bright daylight and with the distance of the subject they were shooting. Flash powder, the system used before flashbulbs, would only have been used in a dark or indoor setting and with a subject just a few feet away.
When the club hostess brings the battered Tom Cruise back to the room, she asks Nicole Kidman about him while she lights a filter tip cigarette. We are in 1895, and filter tips weren't invented until 1927.
More than once, people fire more rounds than their weapons can hold.
The night before the race, as Joseph talks in the tent about how he'll win his land, the tent wall behind him has clearly visible seams that he is supposed to fall through. When he falls and gets up again, the tent isn't ripped, as if someone fell in, it's parted, as if they were sewn that way.
When Joseph and Shannon step off the ship in America, vendors are selling American flags with 50 stars.
When Joseph and Shannon arrive in Boston the American flag waving has 48 stars in the blue background. In 1892, there were only 44 stars on the flag.
A rich aristocrat would have never challenged to a duel a lowlife, that has broken into his house and is already his prisoner. Duels were for honor, that would be degrading himself.