I just wanted to add a paragraph saying that the character in question is not necessarily the protagonist, and that there can be a Double Standard from the audience, in that a protagonist being this tends to be seen as primarily "good" whereas an antagonist is more often seen as just "not nice", ignoring their nobleness.
(This may even be done intentionally, if two such characters antagonize each other, and the audience initially is more forgiving of the protagonist's flaws before noticing that his enemy is Not So Different.)
Inspector Javert may be an exemplar sub-trope of a Good Is Not Nice antagonist.
Unfortunately, either the server or my network connection is somewhat unstable right now, and the site keeps hanging and crashing when I try to edit it. At least I don't seem to have such problems with websites outside ATT.