Continuity mistake: When Johnny, Roy, and Captain Stanley are rescuing the people trapped inside Olive View Hospital, they are wearing distinctively marked SCBA tanks on their backs, and when all three firemen exit the doorway, Cap is wearing an entirely different tank, and the tanks that Johnny and Roy are wearing have been switched. Then when Johnny jumps off Engine 82, his tank differs again, and when he walks over to the Battalion Chief it's changed yet again.
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.