Factual error: Lucas is wearing a pair of jeans with a large "W" stitched on the right back pocket. These are Wrangler jeans, which first went on sale in 1947. "The Rifleman" is set in the 1880s.
Continuity mistake: Mark and Vern sit at a table in the hotel dining room. After they order beef stew, Vern sets his menu on top of a plate. When Lucas enters and sits down, the menu has vanished.
Continuity mistake: The wagon is full of bundles of barbed wire when the boy falls off his horse and into the barbed wire fence. The boy is injured and loaded into the same wagon, that is now completely empty.