Continuity mistake: After Squad 51 is dispatched to the 'injured man', when Roy and Johnny get out of the squad, Roy is not wearing his watch as they're walking to the victim while getting hounded by the dog, but in the next shot the watch is back on Roy's wrist as the dog chews on his pants.
Continuity mistake: In the first episodes, Col. Blake's wife is named Mildred, later her name is changed to Lorraine. (In case of confusion, when Col. Potter came to the 4077th, his wife was also named Mildred, but that's not relevant).
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)
Continuity mistake: As Banacek approaches the room in the farmhouse that has the cross, he has a cigar in his mouth. As he enters, the cigar is gone.
The Gunman - S2-E12
Continuity mistake: The close up shot shows Nedra lowering her head onto White's chest. The next shot is a long shot of her lowering her head on his chest again.