The communication with Superman when he flies to the sun is traveling faster than the speed of light.
Radio waves/electromagnetic waves travel at the same speed as light, and should thus have taken several minutes to reach Superman when he was close to the sun.
Bane doesn't seem to know who Batman is, yet this contradicts the comics. Bane is fully aware of Batman's identity, and the Knightfall story line proves this. The film ignores these events, and makes Bane a dumb brawler, and he is actually one of Batman's most feared and dangerous enemies, he is also quite intelligent and the film simply overlooks this.
After Mirror Master enters the Batcave he breaks into Batman's files, and gains the information for Vandal Savage. Mirror Master even mentions that he would like to know Batman's real identity and Vandel Savage mentions that he knows it already. There is one problem how does Vandal Savage know Batman's real identity??? This is not explained at all, and Batman is one of the most secretive hero's in DC, and Savage should not have known this,this should be impossible.