After Matt hits the window with a rock, the scene turns to Elizabeth at her desk. She turns to the window and walks over to it. Look at the walls and window: The walls are at about a 20 degree angle all the way down, indicating a full attic. When the scene switches to the outside, now you can see the roof is lower pitch, and the window is clearly cut out of the roof. The two do not match.
Right before the wagon explosion, watch how the left wheels go into a small water filled pothole, on the *left* side of the road, at the road and grass boundary. When they pull the camera angle back to see the explosion, the wagon is in the middle of the road, no pothole visible, and the wagon is hugging the *right* side of the road.
Murphy goes to town to buy supplies, and while there he sees Richard Garrett, the deceased Paul's brother arrive in town. After Murphy finds out about the interest rate, he goes to see Richard. Richard tells him to pay it or not charge. In the next Murphy scene, after returning to Gold Hill, Murphy says, "Sometimes I like to grab that Garrett by the neck and pick him up and shake him... I just don't like that man, he is getting more like his brother every day." This does not match the fact that Murphy just met Richard that morning, and Garrett has only been there less than one day.
When Matthew and Elizabeth walk out of the Saloon together, you can see the sun in the background, and the shadows indicate the sun is on the right. But as they progress down the street, the two and pedestrians cast shadows from left to right, the opposite direction.
Check out the spot that Murphy and Moses stop for lunch with Matthew and Elizabeth in the back. They left Gold Hill in the early morning and must have rode for many hours (since it is now noon). This is the same spot used in season 2 episode Buttons & Beaux. In that episode, Lizette walks to work from Gold Hill to Jackson and stops at this location to talk to a boy.
When Matt misses his rendezvous with Elizabeth, he runs from the lake to her house. At the front, he picks up a few small rocks and throws them at the window above the front door. How could he know that is her room when he has never been inside?