Deliberate mistake: When the world is counting down to the new year, we see people in various countries, Egypt, the USA etc all counting down together. Because of time zone differences this isn't possible. [It is a little joke.] (00:01:35)
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.
Slammin' Sammy's Stunt Show Spectacular - S1-E5
Deliberate mistake: Watch the end of the test run for Michael and KITT. Michael was using the KITT steering wheel, but then he gets out of the car and it switches to a performance steering wheel instead.
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: About halfway through the show, Roz and Daphne are in the kitchen talking. Daphne pours water into the teapot - but there is no steam coming from the kettle, nor any sound of a boiling/just boiled kettle. No self-respecting Brit would make tea with water that wasn't boiling.
Deliberate mistake: Robert Brown wears a gold turtleneck sweater with his leather outfit throughout the series. Though it's more than 100 years beyond the show's 19th Century setting, he and the producers decided that he looked good in it, so allowed the anachronism to stand.
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.
Wiegel's New Boyfriend - S2-E2
Deliberate mistake: After the credits, the word "Briefing" is spelled "Breifing" in the shot with the caption "Morning Breifing 6:58 A.M." (00:01:15)
Deliberate mistake: The show regularly shows characters by the Chicago River and either on or near Michigan Avenue, when they are getting lunch or walking to work. Both U of C hospital (where the hospital exteriors are filmed) and Cook Country hospital (where the characters are supposed to work) are about 5 miles from this point. This would be an extremely long distance for them to walk on a routine basis. I'm sure this is done just because Michigan Ave and the river are two of the most scenic parts of Chicago.
Deliberate mistake: These errors I assume were caused by the show running 3 times longer than the real war. Col. Potter arrived at MASH in September 1952 a year before the war ended, then a few months passed by Margaret got engaged for 8 months, then Frank Burns left and Charles took his place. In this time the war would have ended. In the final episode Margaret mentions Charles has been there for 2 years. Which means he would have arrived in 1951 a year before Trapper and Henry left and Col. Potter arrived. It's a lot to take in.
Deliberate mistake: Because Paul Darrow had turned an ankle while shooting the fight scene with Gunsar, the uninjured Avon is inexplicably limping throughout most of the fight. (00:14:00)
Honey, I Shrunk the Rangers: Part 1 - S1-E16
Deliberate mistake: Monkey Bulk & Skull are driving Lt. Stone's car. From inside shots of the car, Monkey Bulk's head doesn't go above the headrest. From outside shots, we can see the guy who was driving the car - his head is way above the headrest, and he's wearing a frizzy fur costume (Monkey Bulk & Skull's fur is very fine).
Deliberate mistake: At the beginning of the chapter, as the scene switches to the surface fighting on Muunilinst, we see a score of droids blasted before the Republic Army's heavy artillery is brought in. But there are no remains on the droids to be seen after the smoke has cleared, whereas there should be something left.
Deliberate mistake: This show is famous / infamous for having many long conversations between characters that are walking the corridors of the West Wing of the White House. In this episode, the chat was long enough that more space was needed to complete the walk, so the actors were instantaneously teleported to a different spot to lengthen the walk. Using http://www.whitehousemuseum.org/special/wwtv.htm as a guide, Pres. Bartlet and Leo leave the Oval Office, pass through the Presidential Secretary's office, turn left, passing between the Roosevelt Room and the Chief of Staff's office. At the end of the Roosevelt room, they turn left through dark wooden doors that are open. Instantly, the actors are at the next junction higher on the map (no wood doors), as if they'd just passed between the Roosevelt room and the Communications Bullpen, and they continue (downward on the map) through the intersection where they original turned (watch for the doors after Leo says "You wouldn't understand"). (00:02:40)
Deliberate mistake: Before each season begins filming, each potential apprentice is filmed leaving Trump Towers and entering the taxi as if they were just fired. Once the person is actually fired on the show, this becomes an obvious mistake as hairstyles, etc. change from the boardroom scene to the cast member's exit.
Deliberate mistake: The credits list "Number 86" as played by John Maxim. But no such character appears in the episode. Apparently, 86 was left on the cutting room floor, but the titles weren't altered accordingly.