Revealing mistake: When Emma hits a man using the flower pot, Angela Lansbury's stand-in is a much younger stunt double.
Visible crew/equipment: When Trish picks up Jessica at the train station and her car leaves, filming equipment and crew members are reflected in the windows.
Murder in the Afternoon - S2-E3
Continuity mistake: The doctor steps in and calms down the actor while placing his hand on his shoulder. A shot later, his arm is lowered.
Murder in the Afternoon - S2-E3
Continuity mistake: When Jessica is in the Lt.'s car, he scolds her, signalling with his index finger, which swaps to an extended hand an instant cut later, which is suddenly lowered yet an instant cut later. The way he holds the car keys also changes.
Funeral at Fifty-Mile - S1-E22
Visible crew/equipment: After Jack's graveside service, Jessica, Mary, and Art walk back to the red pickup, and while they're standing there talking, the mic pops up into view in front of Mary. (00:04:40)
Funeral at Fifty-Mile - S1-E22
Continuity mistake: When Jessica walks from the house to the barn at the end, she is wearing knee high brown boots. By the time she reaches the barn they have been replaced with court shoes.
Continuity mistake: When Ron Moody runs into the sea in pursuit of a suspect trying to escape, he shouts at Jessica to "Get the package!" In the next shot we see Jessica reluctantly follow him in, with a clear waterline from a previous take showing on her dark overcoat/cloak.
Funeral at Fifty-Mile - S1-E22
Other mistake: In the end credits, Jesús is misspelled Hay-Soos, phonetically.
Revealing mistake: When Jessica is knocked down by the kids, she is replaced with a younger stunt double.
Continuity mistake: When Jessica limps into Milton's car, she holds onto the door. A shot later, her hand is away, and it's Milton's hand instead holding onto the door.
Revealing mistake: The newspaper where Jessica is featured has the same paragraphs repeated all the time.
Suggested correction: 1) The text is barely readable even in high definition. (As shown by the fact that you had to blow the image up.) It would definitely be unreadable in the standard definition it was originally broadcast in. 2) The shot is on screen for about three seconds. Not enough time to get through even the first paragraph, even if one was inclined to read it. Freeze framing and zooming in invalidates the error per the rules of this site.
Visible crew/equipment: When Milton arrives at the airport, the filming crew is reflected in the glass on the right.
Continuity mistake: When Milton picks up Jessica at the airport, her bag is hanging over her right shoulder. A shot later, she is holding it with her left hand.
Visible crew/equipment: At the beach, when Miguel jumps in the helicopter, two filming lights are reflected on the windows.
Visible crew/equipment: When Sir John Landry walks towards the fireplace before Jessica unravels the mystery, stage lights are reflected on Jessica's glasses.
Revealing mistake: When Santana is killed, a rectangular pad where the arrow was stabbed protrudes under his shirt.
Revealing mistake: When Miguel tries to sail away, Jessica runs towards the shore. When she enters the water, Angela Lansbury is replaced with a thinner and younger double.
Continuity mistake: When the robber is killed, his hat falls off. A shot later, it's back on.
Revealing mistake: When Jessica is meeting with Congressman Dan Keppner, there are two windows with the Capitol building behind. One can see it's a painted backdrop, most noticeably the window on the left with the garden view.
The Murder of Sherlock Holmes - S1-E1
Revealing mistake: In part 2 of the episode, when Jessica is mugged, Angela Lansbury is replaced with a younger and thinner stunt double twice: when she runs away and when she protects herself against the wall.