In the recent "Blinded" episode of Lie To Me, an interesting thing happens (spoiler alert).
Throughout the show, a support character demonstrates no skill or productivity. He's driven by anger, not by reason, and that anger doesn't help. He's nothing but a burden to the team. One could almost say he's unimportant.
But at the end, a situation arises that suits his aptitudes. Suddenly, this character is the saving grace. In moments, he reveals a few profound insights that lead directly to the team's victory. The sudden departure from his past image is surprising, but believable.
This is a great example of what round characters should be. Authors should know more about their characters than they reveal. It's interesting to audiences when characters make sense but are never entirely known and understood. And character actions are more interesting when they can't be traced to a single origin.
Surprises like this can also encourage the audience to expect surprises throughout the setting and story, to wonder if they've misjudged other characters. Watch that episode sometime to see what I mean.