Deliberate mistake: After Ramsey shows Sansa her flayed northern friend, when it cuts to Davos riding the horse through the encampment one of the shots is flipped. Note his sword and his cloak's crossed straps have switched to opposite sides.
Deliberate mistake: Elsa's dress in Season Four is different from the dress she was wearing in the Season Three finale. The new dress is a different shade of blue, and has a completely different design, even though the present day events of Season Four take place mere moments after the end of Season Three.
Edward Mordrake: Part 1 - S4-E3
Deliberate mistake: After Elsa kicks Bette and Dot off the stage, Elsa looks at the sheet of music on the stand and you see the name of the song 'Criminal' and it also states it's by Fiona Apple which is true, but this season is set in 1952, and Criminal wasn't released until 1996.
Deliberate mistake: Florence and Humphrey set up the scene using a printer that is nothing short of magical; the photos, in color, come out from the machine the instant that Florence displays the profile on screen. It is obviously done to speed up the scene - however, Florence could have printed the pictures beforehand and hand them to Humphrey one by one as she reviews on screen the profiles, there was no need to have them come out fresh from the printer with that kind of impossibly fast timing. (00:15:00)
Deliberate mistake: When Dominique is creating a Tinder profile for Fiona (an app Fiona admits she doesn't use), she manages to use Fiona's phone to take a picture of her, create a profile, and quickly get three matches, all within a span of 25 seconds. Downloading the app itself would take longer than 25 seconds, much less agreeing to its terms of service, and verifying the email or phone number associated with the account. (00:45:15 - 00:45:39)