I well remember the very few scenes in which Columbo loses his temper, but as many have commented, he always has a reason for his behavior. His humility and self-effacement give the villains a sense of superiority and thus make them prone to mistakes. What are his reasons for letting the bad guys/bad gals(?) know he's on to them?
I love Columbo's temper losing moment in A Stitch in Crime. From what I've read, Levinson & Link didn't want to see him losing his rag & very much tried to dissuade his doing so, but I think it really works well - & that moment in A Stitch in Crime is simply superb, really unexpected & hits home so hard that it actually sends tingles down my spine!