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: 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: In the flashback to Angelus rising from his grave, his and Darla's breath is visible as they exhale. This was going to be removed in post-production, but left in due to budget restrictions.
Cold Stones - S6-E11
Deliberate mistake: Tony smashes AJ's front windshield of his Nissan SUV one time with a plastic sports helmet and it leaves a hole 4 times the size. Not only is the scale size of helmet to hole incorrect, but front vehicle windshields don't shatter like that. Modern windshields are made of laminated safety glass, which consists of two curved sheets of glass with a plastic layer laminated between them for safety, and bonded into the window frame. It would've taken many impacts to cause such a hole, not one hit. (00:49:00 - 00:49:45)
Yug Ylimaf - S11-E4
Deliberate mistake: The time machine reverting causes everything in life to go backwards. However, although the characters' actions are reversed, their dialogue is always spoken forwards and not backwards. (00:08:00)
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.
You Wish ('Shanghaied') / Gary Takes A Bath - S2-E11
Deliberate mistake: Spongebob gets stuck in the top of a tree as Gary removes the ladder. In previous episodes it's quite clear that he's more than willing to 'fall' as he takes no damage when hitting the ground due to the low fall speed.
Deliberate mistake: At the very end, Tommy And Merton discover the video tape which contain pictures of Merton that had been film by her sister Beckie, but the movie was filmed and the time ''rewind'' because of the spell. So in reality, the movie was never filmed.