When Batman takes his shirt off toward the beginning to the film, he has a large scar on his shoulder. The scar is gone later in the movie, when he appears shirtless while laying out the clues he's gathered on the Riddler case.
During the wide shot of Gotham City Hall (St George's Hall, Liverpool) 57:53, you can see a bus stop in the bottom right of the frame. This is a Merseytravel bus stop in Liverpool, and being in the UK, the bus stop is on the left hand side of the road, with the rectangle plate on top showing the buses that stop there facing the oncoming traffic.
When Bruce/Batman first gets on his bike his hands are not wrapped but when he gets to Wayne Manor to review the night his hands are wrapped like a boxers.
When Gordon is in a shootout against Penguin and his gang, his car's light cannon is hit. After the pursuit and the interrogation scene, upon leaving the place, it can be seen that the light cannon from Gordon's car is intact.
In the finale, Batman saves people in the water by cutting the electric cable using the knife on his chest then falls in water. He gets out without the knife neither on his chest nor in his hand. The next scene he meets Selina and the knife is back on his chest.
The doctor tells Bruce the she's hoping the patient will stabilize. If he is not stable, he should be intubated and in an induced coma, not just sedated with an oxygen mask on his face.
In the car chase, when Penguin starts to toss around and does quite a few flips with the car, the airbag should be triggered.
The moment when Annika Kosolov's passport is shown on the screen. A birth year is marked as 1998 but social security number starts with 490, depicting that her year of birth is 1990. The passport is issued in 2018 and the issuing authority is marked as KMA (Citizenship and Migration Board). Starting from 2010 Estonian passports were issued by PPA (Police and Border Guard Board).
When GC1 News plays Riddler's latest video (with the victim who has rats strapped to his chest), it uses subtitles for Riddler's voice. The subtitles misspell "judgment" as "judgement," which is incorrect in American English. However, the rule in English is that G can only be soft while preceding an E, I, or Y. This anomaly is derived from a misspelling in an early dictionary and has been propagated ever since. Both spellings are acceptable.
In the scene where Falcone was at the pool table, we can see that the balls change place between two camera shots.
At the very beginning when Riddler is standing behind the mayor, the Riddler yells right as he's making his move forward to kill the mayor, but the mayor doesn't even flinch as someone yells in a room that he thinks is empty. Doesn't react in that moment as the Riddler grabs and kills him. It is a quick moment, but he would of at least flinched.
Slight asynchronized dialogue (obviously dubbed in post-production) when Gordon says "You have any idea what kind of trouble you're in?" at 11:25.
In the final shots when Batman and Selena go their separate ways on the bikes, as Selena drives under the arch towards the camera, the UK road marking for Give Way can clearly be seen on the left lane (from Selena's point of view). Odd production didn't swap for American markings.
Neither Batman, supposedly the world's greatest detective, nor the GCPD, seem to try and search for Riddler's apartment, despite the fact that the photos of the club are clearly taken from an elevated position, rather than from the street.
The forensics officer taking photographs at the scene of the mayor's murder uses the flash when taking photographs for evidence, even photos of reflective surfaces such as the framed newspaper pages. Any experienced photographer would use the ISO and aperture settings to take photographs without a flash, which would eliminate flash reflections and 'whiting out' of the area being photographed.
When Batman handles evidence at Riddler's apartment, Gordon dismisses his concerns by saying that Batman is wearing gloves. The chain of custody concerns go beyond simply leaving fingerprints. At trial, Riddler's attorneys could argue that Batman had tampered with or planted evidence. An experienced officer like Gordon would know all of this.
When the Penguin explains how "el rata alada" is incorrect Spanish and should be "la rata alada", he then says, "¿No habla español, fellas?" But correct Spanish grammar would be "¿No hablan español, fellas?" as he is addressing both of them: the verb should be plural.