When Halloran is looking through the photographs in the murdered girl's room, the page from the bible is folded. It drops to the floor and it is unfolded, in fact it isn't creased. When he picks it up, you can hear him unfolding it before reading it.
Mark Roper takes a shower at the Oakley Park Country Club. It is evident that he is showering in a pair of shorts, and implausibly dries himself enough to be able to put on his shirt and trousers (and presumably underwear) around seven seconds after leaving the cubicle.
The policeman tells a suspect that a blood test can prove the dead girl's baby was his. Unlike DNA (not yet in use), a blood test can only disqualify people accused of paternity; the father could be someone else with the same blood type.
At about 95 minutes, Halloran admits that his evidence would not convince 'the Public Prosecutor'. In English and Welsh law there has never been such a term. Since 1908 it would have been the Director of Public Prosecutions, as any 1957 police officer would have known.
Halloran allows himself to be taken for a turn around the Oakley Park boating lake by Elizabeth, but the camera/background shakes more violently when on him (physically rowing the boat in the location footage) than when framing his more sedate companion (in footage shot separately).
The bundles of 'newspapers' being handed out by the Newsagent to the paper boys in one scene are obviously bunches of blank paper.
When Dr Fenner admits Roper into his consulting room, his mouth is visibly moving as he closes the door, but no dialogue accompanies him on the soundtrack.
Superintendent Halloran identifies the key Bible quote (given as the somewhat bowdlerized and abridged "And Aholah played the harlot when she was mine; and she doted on her lovers, and they discovered her wickedness and they slew her with the sword; and she became famous among women; for they had executed judgement upon her") as coming from Ezekiel 24. In fact, it appears in Ezekiel 23 - though this may be an attempt to trip up the murderer he suspects is in the room with him.