Continuity mistake: When the cop picks up the dirty ashtray he blows the ash away. In the close-up the ashtray is spotless as if it had been wiped with a cloth or if it were brand-new. First of all, no ash blew away, and second of all, a mere puff couldn't have cleaned it the way it looks.
Plot hole: Barney Kale decides to reopen a case he couldn't solve. Based on the outcome it makes no logic whatsoever. He is the murderer. Why would he bring attention to it put himself in danger? (00:46:50)