Regarding the police stupidity in their chase turning from Bane and chums (a less successful Saturday morning site than Lothar and chums) there are two points if like to raise:
1) 'Harvey Dent Day' was very recent (a few days earlier at most) so the mysterious disappearance of Batman having allegedly killed their White Knight would be fresh in their memory.
2) These are peace time police who have proved themselves to not be as diligent as they once were, except for Blake: the wonder cop. After 8 years of not much to do after the Harvey Dent Act they'll be looking for political point scoring to prove themselves. Catching Batman is THE big fish.
But still...what a douche