Deliberate mistake: When the Doctor begins to "fade" in the transporter room his mobile emitter fades with him. Since it's made of solid matter and is not a hologram, this shouldn't be possible.
Tabula Rasa - S1-E3
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.
Mr. Monk Meets His Dad - S5-E9
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: The final Auton attack in this episode is supposed to take place in a busy London street, but it is a pedestrianised area, and several shots reveal this. For example, there are no road markings visible, no apparent distinction between pavement and road, and a bus stop appears to sit in the middle of the 'road'.
Deliberate mistake: Every time the commandos are seen in the early episodes of this season (The Freshman and Fear, Itself) they wear ski masks to protect their identities. Starting in The Initiative, they stop doing this. The reason is that the audience needs to be able to identify the different commando characters, but it's still a discontinuity.
Deliberate mistake: The dying Vantika hides his consciousness away in a portion of Dr. Bashir's mind. At one point, "Bashir" (heavily cloaked in clothing and shadows) comes up behind Quark and makes sure his demands are clear. At this point, it should still be unclear just how Vantika is still "alive", and whose body he is using. However, when he shoves Quark away, for a fraction of a second, Bashir's face can be seen under his hood. They were true to plot in using the right actor (though he shouldn't have been seen), it is possible some might have spied the secret earlier than the show meant to reveal it.
Deliberate mistake: At the beginning, Asajj Ventress is wearing an outfit with a long skirt. When she is rescued from her damaged starfighter by the scavengers, the skirt has vanished. This was done because the animators found the skirt too difficult to animate. This is also why she receives a brand new outfit that never had a long skirt later in the episode. (00:08:20)
Deliberate mistake: Although it is later revealed that Sarah is the intruder, the person fighting is male.
Deliberate mistake: Lindsay is not at Caleb's funeral in the last episode of season 2, "The Dearly Beloved". It's unlikely that she would have missed it - she is still on good terms with him and he is her father, the only reason she left was to be with her mother, not because she didn't love Caleb.Obviously they didn't want to create another drama with having Lindsay there while they had to focus on the important story-lines - Caleb's death, Kirsten's drinking and Marissa shooting Trey.
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: Rampart's ER is located in the south lower wing of the hospital complex and it is only a two-storey building (with a basement), but the elevator, which is located past the nurses' station at the wing's far south end, has two floor indicator panels listing eight floors - one panel over the elevator doors and another we see every time the elevator doors open, which is not possible.
One Breath - S2-E8
Deliberate mistake: When Scully is shown on her hospital bed, it's obvious she's wearing a bra under her hospital gown. It's doubtful that a patient in a coma would be wearing a bra as it could restrict her circulation.
Deliberate mistake: Clark's CPR form is terrible. When he performs emergency breaths on Lex, Lex's chest doesn't rise and fall, indicating that he's not actually breathing much air in. He doesn't bother to measure for the proper location for chest compressions, a very important step that is the difference between proper CPR and simply cracking ribs. As he performs compressions, he is not chanting the rhythm (one-and-two-and-three) and his elbows are bent. All of these were altered for dramatic reasons or the purpose of safety, but the sloppy technique probably would have killed Lex. (00:18:40)
Day 2: 6:00 P.M.-7:00 P.M. - S2-E11
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: After the Crazy Ivan, where they escape from the Reaver ship, the shot of Mal, Wash and Zoe celebrating on the bridge. Wash has his hands out in front of him like he's still holding the stick, but there's nothing in his hands. In the commentary, Joss Whedon mentions that, in order to get the shot right, they had to move the seat back far enough that Alan Tudyk couldn't reach the controls, so they instructed him to mime it.
Deliberate mistake: In the episode where Mary-Alice Young's house is open for buyer's inspection, the phone number on the "For Sale" sign has been digitally blurred.
Deliberate mistake: 9-12 "The Bells Toll at Noon": When McGarrett picks up Danny and drives away in his Mercury Grand Marquis, the rear view mirror is missing, probably removed to prevent it from blocking the actors' faces. It reappears later on. (00:33:00)
Deliberate mistake: During the 6/11/04 episode, Jax and Courtney are having dinner in Italy. Carly, who is in New York, does some sleuthing, finds out where Jax and Courtney are, and flies to Italy. Miraculously, Carly manges to fly from New York to Italy and arrive while Jax and Courtney are still eating dinner.
Pilot (aka Emotions in Motion) - S1-E1
Deliberate mistake: Throughout the first episode, Jen's bangs are long in scenes relating to her "Grams" and short in all other scenes. This is because the scenes involving her storyline with Grams was shot much later, after the show was picked up. (00:05:45 - 00:16:15)
Deliberate mistake: Though he moved freely about the station in his environmental suit, Kosh was never actually seen going through a door. He approached doors, but then, sometimes rather disconcertingly, would suddenly be shown on the other side. The reason: look closely and you'll realise his costume was too large to fit through any of the doorways on the set, so in reality the character would never have been able to move around the station.