Deliberate mistake: As Ray drives the pickup truck, an oncoming vehicle beeps and the marshal heads behind Ray's pickup. In the shot through the cab's rear window facing the bed, as the marshal pulls behind, the bed's side wall interior is seen (note the metal loop tie down on top) and the entire tailgate is gone; yet the tailgate is intact later, when the pickup flips over. The tailgate was removed for the shot to allow visibility of the marshal's vehicle.
Deliberate mistake: In the opening scene, Wood's tie is grabbed by an exposed fan belt located above the side of the engine. However, this belt/pulley assembly doesn't exist in a real truck's engine compartment - the fan belts are all in front of the engine, where the camera can't see them easily. The prop master must have added this dangerous device to the truck to allow the camera to see the strangulation.
Deliberate mistake: Every time the investigators deal with IP-addresses, the addresses on display are impossible. Each of the four parts of an IP-address has to be between 0 and 255. As they do have to use IP-addresses some time, they could use addresses starting with 10. Those would be real addresses although not used as an official IP-address. This isn't the same as phone numbers using 555 - any IP address over 255 just wouldn't work. It would be like mentioning a phone number which uses the symbol for pi.
Deliberate mistake: When Jack and that FBI team are looking for Sied Ali in the mosque, Jack finds a burning body in another room. He is led to believe that it is Ali, because the body's clothes matched the description that Kate Warner had given him. It is obvious that the skin is badly burnt, yet the clothes are barely scorched.
Deliberate mistake: Garrity blackmails the town citizens into paying him not to resurrect their unlamented "loved ones." Amazingly, every man in the saloon just happens to have hundreds of dollars ($500 - $1200 each) in his pocket to pay up with. In 1890 money, that's roughly equivalent to a group of modern-day bar patrons all carrying ten to thirty thousand dollars around in their pockets. The scenario was apparently used in spite of its incredibility just to more quickly advance the plot.
Deliberate mistake: Kermani finds a nitroglycerin tablet in the suspect's apartment. Because we need to see it when he holds it for the close-up, the tablet he has is much too large to be nitro. That drug is dispensed as an extremely tiny pill designed to dissolve instantly under the tongue. (00:22:30)
Deliberate mistake: When James is shot on the courthouse steps, the crowd of reporters that has gathered quickly scatters to escape the gunfire. One of them is a woman in a black windbreaker holding a camera. The camera cuts away briefly and then back to the crowd - you see the exact same people, including the woman in black running in the exact opposite direction as before. The footage was apparently mirrored and repeated for the second shot of the fleeing crowd.
Deliberate mistake: "The Creature's Revenge" (Adventure 3, Part 5): The 2-inch heels on Sapphire's bright blue boots disappear and reappear repeatedly. They're most often missing in the scenes she appears in with Steel, presumably so that her height won't exceed his. (00:15:15)
Deliberate mistake: When the investigators are in the basement wine cellar, they turn on their flashlights to illuminate the pitch black area as they walk around. However there is a light source moving with the camera shining on them as they are casting a shadow behind them.
Deliberate mistake: When a patient who is given CPR is seen in the shot, the person giving the CPR does so with bent arms (the correct way to do it is with straight arms). This is deliberate, as straight-arm CPR puts in an amount of strength that frequently breaks ribs. Many films do CPR with bent arms rather than straight to avoid harming the actor.
Deliberate mistake: During the big battle, Arrow is knocked down and when he opens his eyes, the reflection in his eyes is tilted over to give the sense he's seeing things sideways. But the reflection should still have shown the proper orientation no matter what orientation his eye was at. Think of looking into a mirror and then rotating the mirror to the side, the reflection wouldn't rotate.
Deliberate mistake: The army major wears a full beard. British Army personnel may not wear beards. (The beard is a nod to the original canon character on which he's based, John Barrymore, who is described in the book multiple times as being a "black-bearded man").