Police work, questioning the methods

In 1962 you would not find fingerprints on a food box or any type of paper surface. This is a common mistake in films, because it's not understood that obtainable prints, up until the 90's, must be on a smooth,clean, hard surface. The suspect leaves body oils and when touching an even slightly dusty surface, the suspect takes away, not deposit fingerprints.
Additionally, finding a suspect with a found fingerprint, was a long and labourious task, often lasting several days. Of course they had people they suspected, so they could add or eliminate them.
Since the film was based on a real event, it seems it should be bound to reality.