Continuity: When he hits the ball off the clock, everyone leaves the park after his home run. Why should they? Roy Hobbs' team is the visiting team, so the Chicago Cubs still have their turn at bat in the bottom of the ninth.
Great sites
Mistakes
When Roy breaks his bat in the playoff game, the bat is a long way from the batter's box; the "Wonderboy" fragment is lying further away from the foul line than the rest of the bat, and the fragment "point" faces away from the foul line (hard to see in the long shot, but note how Savoy hands Roy the fragments by both barrels). However, in the close-up the point is beside the foul line, as are the two other pieces. See more...
The Natural mistakes
Continuity: During the scene in a coffee shop or diner after Glen Close has come to see Robert Redford play baseball, her coffee cup and saucer disappear and reappear throughout the entire scene.
Continuity: In the newspaper clippings of Hobbs' feats, the words under the headlines talk about government proceedings - not baseball.