Disguises: tattooed sailor, waiter, elderly postman
Gadgets: thermite string, underwater mini-explosive, pocket blowtorch
It's clear by the lighting that when Jim is swimming inside of the indoor "tank," he is in fact outdoors in a pool or reservoir of some sort.
In one particular underwater scene, there is a clear picture of a guy in a scuba-diving suit. It's also clear that Robert Conrad is swimming in an aquarium of some sort since the concrete walls can be seen behind him, despite the fact that he's supposedly in a natural lake. Then there's the time when West comes up for air...and his hair is dry!
Gadgets: burning powder to cut through a wooden floor, thermite lock-opener
Disguises: condemned prisoner Aaron Addison, man in fez
When Jim uses the powder in the attic, in the close shot he kneels and his right knee is in front of his left foot. The camera cuts to a middle shot and Jim's right knee is now in back of his left foot.
The episode opens with Jim with his new look and shorter hair. Later when Jim is running to escape the men chasing him, he walks from a garden gazebo through a secret passage leading into a nearby house. When he exits the corridor and enters the house, his hair is full-grown again. When Jim jumps out the window, it's back to the shorter look.
When Jim hides in the morgue drawer, he's able to open it from the inside. Although somehow he gets it open without moving his hands or feet. However, later the attendant is unable to get out of the drawer that Jim puts him in.
During the wagon chase, footage from some other movie or TV show is used. The wagon only has a single driver up front in the stock footage, but in the closeups Jim and Artie are seated next to each other. Also, the men following on horseback are in cavalry uniforms, not the green-shirt Black Legion uniforms. Finally, Jim and Artie jump off on a curve with a great deal of brush, but when the troopers in the stock footage ride past, the area is clear of foliage.
Trivia: This is one of the rare episodes where neither agent uses any gadgets.
Disguises: Joe the piano player
When Jim and Artie find Cole's recently dug grave, the earth is flat. A recently-dug grave would have the excess dirt taken up by the body somewhere nearby, but it's nowhere to be seen.
Jim is in Wyoming and sends a telegram to Fort Savage requesting assistance. However, in "TNOT Firebrand," Fort Savage was on the Canadian border in the state of Washington, adjoining British Columbia.
The man on horseback when Artie jumps over the barricade is clearly not Ross Martin, being noticeably younger and thinner.
When Cassidy shoots the clock in the store window, after the glass cracks, a brief reflection of a crew member can be seen in the glass.
Gadgets: strap-on palm hooks for climbing, derringer dart and line w/pulley handle
Artie has a three-ring binder to keep his notes, as can be seen on the train after the attack on Jim. Ring binders weren't invented until 1886, nine years after Ulysses S. Grant left office.
Artie mentions that Sinful is part of an arc that connects Salidas, Rome Plateau, and Tonka Flats." Apparently a scene was cut, because the significance of the first two cities is never explained on-screen.