Deliberate mistake: Although it is later revealed that Sarah is the intruder, the person fighting is male.
Second City - S1-E12
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: Very often, during Skype or other video chat conversations, the people on the computer screen look left or right when talking to someone who is not directly in front of the screen. Although it certainly helps the viewers understand who's talking to whom (which is why I assume it's a 'deliberate mistake'), it isn't realistic, since it implies that the people on the screen are actually constantly looking away from their computer instead of at their screen or webcam.
Deliberate mistake: Around the 26 minute mark, when Charles Brandon joins Margaret for a game of cards during their voyage to Portugal, Margaret has a glass of wine (and later Brandon) in which the liquid is not sloshing around As It Should Be on a ship that is rocking and swaying the way it should. (00:26:10)
Wizards vs. Vampires on Waverly Place - S2-E26
Deliberate mistake: Justin tells his dad he will write the idea on the white board (the theme in the restaurant/add more of an experience) yet he just scribbles, and in the scenes where you see a bit behind him, the whiteboard has scribbles instead of words where he was supposed to write.