When Joe is talking to Phil about a new story angle on him, in a closeup shot, Phil is talking to Joe with a cigarette in his left hand, waving it around. In the next wider shot, Phil has his left hand in his pocket, and the cigarette is in his right hand.
When the corpse surfaces on the lake, it appears feet first. In reality, the torso would rise first, because it is full of gases that make bodies float. The legs are only muscle, bone and connective tissues, with no way to produce or retain gases that would encourage floating. However, as noted in the narration, there was a slot machine chained to the body. A slot machine chained around the neck or shoulders would allow the corpse's feet to break the water's surface.
When Nicky goes to rob the liquor store, the door has deadbolt hardware on the inside and outside, but there is no corresponding bolt or plate on the edge of the door - an obvious shortcut taken by studio carpenters.