When Jonesy leaves his apartment in a rush he forgets to turn off the taps and his tub is (torrentially) overflowing. But when he returns from the police much later in the day there is no water anywhere.
After Mannion (disguised as Jones) leaves prison, a newspaper headline says he shot and killed Martin. For one thing, there's no way he could have smuggled in a gun; for another, a shot would certainly aroused suspicion, and finally, when Mannion returns, he's wiping his hands with a handkerchief, confirming that he likely strangled him (which of course would have made no noise except for perhaps a muffled shout).
When Jones enters his apartment after being escorted by the police; Mannion is sleeping with his head leaning to the left shoulder. But on the next cut; his head has changed orientation. It is now in the middle and no longer leaning.
When Jones returns to his home; Mannion is waiting for him and is holding a pocket watch with his left hand. But on the next immediate cut, Mannion is now holding the watch with his right hand.
The story under the newspaper headline about Killer Mannion escaping from prison bears no relation to the headline and opening paragraph.