Cognitive dissonance is experienced when a person become aware of his/her own hypocrisy. In most cases, people will either try to justify the behaviour to match the thinking or vise-versa, depending on what the path of least resistance is.
I have no qualms with cognitive dissonance because I often know how to resolve it. Justification takes effort, yes, but it's easy. Just think about it. The last time you did something against your morals, you felt horrible right? How long did that uneasy feeling last? I'm sure whatever guilt or shame you experienced was diminished quickly, either by behavioural compensation or a set of self-affirming thought procedures. Either way, cognitive dissonance didn't plague you for long because in reality we hate the identity of being a hypocrite.
What's scary about cognitive dissonance is that it can potentially develop into doublethink if one does not arrive at an adequate justification for their incongruent beliefs and actions or willingly accepts the hypocrisy for the sake of easiness. If you've read 1984, you're familiar with that term. The very idea of doublethink sparks in me another explanation for contemporary "social malaise" - the breakdown of moral codes and the alienation of people from each other. Doublethink is partially responsible for a wide range of antisocial behaviours observed in individuals as well as conglomerate groups (ie. corporations). It also accounts for the mind-boggling inhumane acts performed by otherwise an average person (bounded by the basic moral codes). It has the potential to infiltrate even the most just individual but it can be made aware to the person and devolve back into cognitive dissonance. This would be ideal, though uncomfortable, but at least you'd still be able to something about it. And that to me is more important than anything else - being able to still do something.