The alloy wheels on Beth's Jaguar frequently change between two different designs from scene to scene. The Interior also changes, notably the head restraint and steering wheel design. It clearly indicates there were at least two cars, one early model and one later model.
Sarah pulled Paul's belt off in the kitchen, but it was in the trouser belt loops the next morning.
When Kira donates bone marrow, Delphine is told to wait outside by Siobhan. In the next scene on the subject, Delphine is in the room with Kira.
Katja Obinger's birth certificate, which is shown when Sarah searches the contents of the safety deposit box, is apparently issued by the German Democratic Republic but states the city of Würzburg as Katja's birthplace. Würzburg was in the Federal Republic of Germany.
Katja Obinger is supposed to come from Berlin. Her birth documents say "Würzburg". The same documents are issued by the "Deutsche Demokratische Republik" (GDR) but Würzburg was not part of the GDR, it was West Germany. The birth documents also show the birth month as "March" - as a German paper it should have been "März". Finally, German birth documents are not printed in A4: they're in an special format that can be filed in a ring binder.
Police, like most security professions (i.e bounty hunters etc.,) have their fingerprints taken and added to the state or national database. Childs on the slab would have been identified as the cop by the medical examiner immediately.
The birth certificate of Katja Obinger is shown on screen, stating "Würzburg" as both the city of birth as well as the city where the certificate was issued, but the character Felix says she was born in Berlin.
Both of the main British characters routinely use the swear "f*c*ing shite" pronounced with a hard i like in "bite" instead of "bit". Only Northerners, Scottish and Irish do this. Although Felix and Sarah are from London, they were raised by Siobhan who is Irish, it's likely they inherited some of her language in childhood.