The positioning of the vinyl albums arranged on display around the room when Sam calls in on Layla.
Layla is supposedly three months pregnant when she gets her ultrasound. The fetus shown in the ultrasound image is much larger and more developed than a fetus would be at twelve-to-thirteen weeks.
The Manchester CID claim to have no knowledge of heroin. But by the mid 1970s, heroin (stolen from doctor's surgeries and chemists, as it was still being prescribed) was a known drug in the jazz and rock scene. There were private clinics dealing with addicts, and while it wasn't as huge in 1973 (when the episode is set) as it was in 1979 (when use in the punk scene escalated), the Manchester CID should have been completely briefed and known about heroin.
The series is set in 1973, In the record shop scene a record called "Music Explosion" is on display but this record wasn't released until 1974.