At the start of the story, the police enter the suspects house and state they have a warrant to search the premises. A warrant is not necessary in these circumstances as once the suspect has been arrested, the place he was detained or immediately before can be searched under Section 32 PACE (police and Criminal Evidence Act 1984).
Bascombe tells Jamie that Katie was found about 10:30 PM and that when paramedics arrived, they could not stop the bleeding. He then advises she had been dead less than an hour prior. However, he actually says "was killed less than an hour before" to indicate that the wounds she ended up dying from after the paramedics arrived were inflicted in that time frame, not that she was already dead at that point.
Jamie puts his jumper on the wrong way.