Deliberate mistake: In the opening scenes just after the restaurant dialogue, as soon as the scene changes there is a quick cutscene which shows the screen zooming in on the Pentagon. If you look In the lower left corner, the text on screen gives the Pentagon location as being in Washington D.C. however, The Pentagon is located in Arlington, Virginia. (00:19:02)
Deliberate mistake: When Batman enters the replica of The Joker's apartment there's no place for The Joker to hide. Yet seconds after Batman enters, The Joker comes out of nowhere to hit him with a pot.
Deliberate mistake: It is unlikely that Kimmel shoving/ramming the beer bottles on the table using his dish and piece of steak in his right hand would shatter the beer bottles into such small pieces (or at all) like he did. (00:36:55)
Deliberate mistake: Where are the motorcades for the other world leaders?