2) British police do not 'read him his rights' - they ensure that the arrested person is cautioned. “You do not have to say anything. But, it may harm your defence if you do not mention when questioned something which you later rely on in court. Anything you do say may be given in evidence.”
3) They have no 'badge' - they carry 'a warrant card'.
4) Superintendents, by and large, do NOT investigate.They sit in offices.
5) Inspectors do not trail around with a sergeant in tow.
6) Serious crimes are largely investigated by sergeants and the multitudes of PCs who get forgotten by so many writers.
7) Detective inspectors - and very occasionally one notch above - will sift through information gathered with an overview.
8) Dig out old episodes of The Bill on Drama channel to get a pretty fair idea of how things work - but even they blow it occasionally. Two sergeants going out together to investigate or go door to door is absurd.