During the hunt, Charles fires his rifle twice, only a few seconds apart (we see the first shot, then the camera cuts to Edwards when we hear the second one). The two shots sound different even though they came from the same weapon.
While the electric chair was introduced in New York in 1890, information given in previous episodes shows that this takes place in at least 1891. In season 5's There's No Place Like Home: Part 2, Lars Hanson told Doc Baker he had settled there and founded Walnut Grove 50 years ago. A sign shown at the end says Lars founded the town in 1840, which would put The Return of Mr. Edwards in 1891 or later.
"In this story, Mr. Edwards loses a leg and tries to kill himself. Yet, after he comes back to the show as a regular, he has both legs through the end of the series."
While Mr. Edwards does refer to himself as being 'half a man,' he still has both of his legs, with one of his legs being broken, not missing. This can be witnessed when he is getting off of a horse and both of his feet are firmly on the ground despite using a crutch.