Beckert’s knife (situational irony)
When the serial killer Beckert is talking to a little girl, he suddenly pulls out a switchblade out of his pocket. Upon seeing this knife, the audience thinks that Beckert is about to commit another murder. Instead, he uses it to peel a piece of fruit. With this reversal, Lang masterfully manipulates audience expectations and foreshadows Beckert's later claim that there are two men inside him: one who kills and one who is terrified of the killing.
The Blind Man Catches The Murderer (situational irony)
The whole city—the police, the underworld, an army of street people—search for the child murderer, yet it is the blind vendor who ultimately discovered Beckert, thanks to a tune Beckert is in the habit of whistling. This adds a fairy tale element to the story. It additionally reveals some alienation latent in urban life, as the murderer otherwise blends in with the masses of men who sport near-identical top coats and hats.
The Police Investigation
The police seem to leave no stone unturned in their hunt for the murderer, yet generate no significant leads. We first encounter the investigation as a farce involving a psychologist making grand assumptions about the murderer based on his handwriting, and an investigator musing about the killer's profile based on his blown-up thumbprint. We expect the police to be masters of detection, and yet they are totally inept; it is the criminal underworld that proves capable of finding the murderer in just about no time at all. Lang doesn't use this irony to make some grand political point about the Weimar government, but as part of an allegory diagnosing why his fellow Germans have grown so jaded with official recourse that they take to the streets in search of retribution. This failed police investigation is a big part of M's damning allegory about how the breakdown of government and civil society set the stage for fascism to take hold.
Beckert In Custody (situational irony)
From the time that Beckert is cornered by the gang through the end of the movie, Lang uses classical narrative filmmaking devices like close-ups and heroic low angle shots to drive audience sympathy with Beckert. Obviously, this is deeply ironic given the fact that the entire movie up until this point was devoted to the hunt for this clearly atrocious individual. Lang plays our sympathies like a fiddle to ask whether a monster can still be a human who deserves basic rights, and if mob rule against such a man is really justice at all.
