When can an angry mood be beneficial?

Anger focuses attention on rewards, increases persistence, makes us feel in control and more optimistic about achieving our goals.

Via The Science of Sin: The Psychology of the Seven Deadlies (and Why They Are So Good For You):

So what does anger actually do? When Ford examined where participants spent most of their time looking, he found a clear bias toward rewarding stimuli. It was the erotic couples that seemed most interesting to the angry participants, not the knives. By comparison, and as expected, fearful participants were biased toward threat. Neutral participants showed no bias either way.

The monk John Cassian was afraid that anger would blind us. But it doesn’t so much blind us as put a particular brand of functional blinders on our perceptual systems, redirecting them to what is relevant in the environment. When angry, we focus on rewards. And it is this focus that partly explains why we persist in the face of adversity. If we encounter an obstacle while pursuing a goal, anger directs our attention to the rewards of reaching our goal and so breeds perseverance.

And:

The emotion that participants happened to be feeling at the time significantly impacted their risk perceptions: Angry people were more optimistic about their futures than were fearful people… angry people also saw future events as more controllable than did the fearful. The researchers also showed, statistically, that participants were more optimistic because they felt more control.

Such mental shifts are probably what account for the performance benefits attributable to anger. Although our trajectories toward a goal might be momentarily blocked, by focusing on the potential payoff rather than ruminating on our failure, anger prompts us to persist. When we experience this emotion, attention narrows to focus on rewards, and we also have a sense of greater control and optimism, making us think that we can actually attain those rewards.

And angry music can boost performance:

What Tamir and her colleagues found was that people preferred to listen to the angry music before playing Soldier of Fortune. Faced with a task in which anger might serve a useful function, facilitating the shooting of enemies, participants opted for an anger boost. What’s more, listening to the angry music actually improved performance…