Tartuffe, in Moliere's play of the same name, represents many vices, indeed, criminal behaviors, having committed so many crimes as to be arrested by a Gentleman of the Guard! Among these would be fraud and false witness against innocent individuals, i.e., Orgon. The vice that Tartuffe is generally associated with, in relation to the theme primary of the play, is hypocrisy.
The primary theme of Moliere's satire is religious hypocrisy versus true Christian values. Tartuffe is the representative of hypocrisy while Cleante is the representative of true Christian values, and Orgon is the one against whom the definitions of these terms is played out, making for a rather neat plot device.
Hypocrisy in our era seems a small vice because it is a common epithet to bestow on people who don't always behave according to church traditions or who feign friendship. But the way Moliere paints hypocrisy, he means it as a grievous act of serious proportions.
"Values" also seems a modest sort of word in our present age but when cast in an analogous position next Tartuffe's style of hypocrisy, "values" takes on much larger scope than the lifestyle choices that "values" is generally associated with today.
As in the above, the problems Tartuffe represents are many: insinuating oneself into another's affections and good esteem on fraudulent grounds; manipulating individuals to gain selfish ends; willfully misrepresenting yourself in order to take advantage of someone's position. However, the main problem Tartuffe represents is that of defrauding an entire family out of its rights and happiness: a daughter wed against her will, a son disinherited, a wife made the object of ghastly attentions.