The Search - S4-E15
Continuity mistake: When John borrows Vern's blue car to search for Olivia and the kids, its license plate number is "45-2678" in wide shots, but when John-Boy spots their truck at the side of the road John stops short, and the license plate number is "84-6209" in the closeup. (00:17:10 - 00:18:45)
The Secret - S4-E16
Continuity mistake: Jim-Bob's birth certificate reveals he was born January 13, 1923; however in Season 3 The Runaway Jim-Bob says his birthday was June 13, 1924. John-Boy was born just before when John was going off to WWI (1917-1918). If Jim-Bob was born at The Beginning of 1923, that would make him 5 years +/ - younger than John Boy. We know that Ben, Erin, Mary Ellen and Jason are all older than Jim-Bob.
Continuity mistake: When Ben first sees The Fox in the box trap and rushes over, both the y-branch and straight branch are lying atop the box, but as Ben kneels down now the y-branch is instantly upright with the straight branch still lying beside it, then Ben's siblings run over. (In the next shot, as Mary Ellen mentions Carol Lombarde, the box trap is suddenly set atop two saw horses with the two branches set in their trapping positions. This change is quite abrubt between the two shots and presented as if they have not moved). (00:29:40)
The Secret - S4-E16
Continuity mistake: The view outside Johnboy's bedroom window is a tree within feet when no such tree exists in prior episodes. In fact, all the bedroom windows face the driveway.