Deliberate mistake: At the end during the car chase, the blue car goes under the lorry trailer. All tailors are fitted with safety side bars to stop this happening, they have been deliberately removed for the action scene.
Deliberate mistake: When Lex busts Joker out of Arkham Asylum, he uses his Deconstructor gun on the LEGO wall. It takes it about 8 seconds to pull the LEGO apart for Joker to get out. The same amount of time is taken when he demonstrates it to Joker and frees Penguin. Yet when Joker grabs it and uses it to free Catwoman and Two-Face, that time is cut in half. And then yet again when they are leaving on the chopper, Joker fires it 3 more times, freeing Poison Ivy, Harley Quin, and The Riddler. It barely takes a single second on each of those. (00:17:40 - 00:19:35)
Deliberate mistake: Hansel will die if he doesn't take his medicine for 4 hours, but after hanging overnight in a tree he shows no signs of needing.
Deliberate mistake: After the AN-12 launches from the carrier, you see U.S. Navy near the nose of the craft, and MG on the tail code (MG=McGuire Air Force Base). Also, during the flight shots, the plane transforms between a C-130 and AN-12 multiple times.
Deliberate mistake: In the scene where Mindy saves the dressed-up Dave from the street thugs and almost gets caught by the police. The female voice over the police radio remarks that the suspect is "under five feet" (below 152 cm). As she flees, she uncovered her motorcycle which appears to be a Ducati 1199 Panigale. The Panigale has a seat height of 82.5 cm, which means that by proportion, Mindy cannot sit on the bike with both feet flat on the ground (as a comparison, I'm 5'9 / 175 cm and still have to tiptoe a little bit on the Panigale, so even if she's slightly taller she still couldn't). Yet in the end scene where Mindy drops Dave at home after the final fight, she seems to be able to sustain the bike with both feet only slightly tiptoed, although her boots are not that tall. (00:13:20 - 01:34:30)