Firefly (2002)

The Message - S1-E15

Continuity mistake: At the beginning of the episode, when Jayne reads in the note from his mother that she enclosed something in the box for him, there is a shot of Zoë reaching for a crowbar to open Tracey's coffin. Jayne's left hand is visible on the far right of this shot, holding the hat that his mother knitted for him. In the following shot he takes the hat out of the box despite already having it in his left hand in the previous shot.

THGhost

The Message - S1-E15

Continuity mistake: At the beginning of the episode, Jayne receives a hat from his mother in the post, and when he takes it out of the package it is covered in wood shavings or some similar packing material. He puts it on his head like that, but for the remainder of the scene, the hat alternates from being covered in shavings to clean and back again.

STP ★

The Message - S1-E15

Continuity mistake: The cut the doctor makes on Tracey is small, but once Mal is on top of Tracey, the cut is a lot longer.

Cybermoose

The Message - S1-E15

Continuity mistake: In the first scene in which the crew is back on Serenity, they are discussing Mal and Zoe's recent "delivery." Jayne is shown taking his hat off. Two shots later Jayne is shown in the background with the hat still on his head. Six shots later Jayne is shown with his hat in his hand again.