I will not deal about the plot, which you can easily pick up from elsewhere, and focus rather on my own critical impressions as a simple viewer.
To state it in a sentence: if you decide to abstain from more precise puncualizations you can still enjoy the film.
The main problem (minor flairs are also present) is: evidence is lacking, both when the first suspect is sentenced to death, and when, later, the two amateur detectives - by sheer luck - come across some clues that make them assume (without any certainty, again) who the real murderer might be. The filmmakers were undoubtely aware of that impasse, as the only way they could possibly conceive to make clear who really "did it" is the criminal's own confession.
To state it in a sentence: if you decide to abstain from more precise puncualizations you can still enjoy the film.
The main problem (minor flairs are also present) is: evidence is lacking, both when the first suspect is sentenced to death, and when, later, the two amateur detectives - by sheer luck - come across some clues that make them assume (without any certainty, again) who the real murderer might be. The filmmakers were undoubtely aware of that impasse, as the only way they could possibly conceive to make clear who really "did it" is the criminal's own confession.