Weiner has made it easy on us because of his reaction to the affair's discovery: not only denying it (that is natural, albeit wrong), but actively accusing Andrew Breitbart of smearing him. Anybody who can lie so baldly definitely deserves to be out of Congress, Republican or Democrat.
Then there is the question of whether he knowingly flirted with underage girls, as it appears he may have come on to a high school student that he met at a rally. Then there is the question of whether he might have done anything besides just sending pictures and lewd texts, or whether he intended to do anything...
But let's leave those questions to the side and focus on the issue of whether a married Congressman who flirts with other women deserves to lose his seat. There is flirting and there is flirting. I tend to think of flirting as things like being overly attentive to someone or making sexual innuendo, and while those things are dangerous to a marriage, they don't rise to the level of cheating, or at least they might not, depending on the context. Saying "you make me hard" and sending close-ups of your groin clad only in underwear is a different sort of thing. To me, it clearly expresses the desire to cheat, and, even if the person never intends to follow up on the desire, I would not trust him (or her) alone with the flirtee for 10 minutes. I would not trust him alone with any member of the opposite sex for 10 minutes. The other kind of flirting may be the same thing by a more discreet, or just plain scared, person, but it could also be just playful -- again, the context matters.
Still, neither is quite the same as cheating; it is certainly worth making a distinction between having sex and talking about having sex. How does this rate in the scale of transgressions? It is certainly a transgression, although many Democrats have tried to dismiss it by pointing out that Weiner has never tried to regulate other people's morality. They overlook, or willfully ignore, the fact that Weiner took an oath of fidelity to his wife (and not all that long ago, from what I gather). If he were single, or if he had an open marriage, the "no hypocrisy here" defense might work. In his case, it certainly does not. Politicians tend to be married, and they tend to derive political advantages from their marriages, or at least they think they do. I think we are certainly entitled to consider a person's fidelity as part of an overall evaluation of his fitness to serve.
Weiner's shameless and tasteless self-promotion -- sending out pictures to unwitting women to see if he could get a positive response -- make this a more egregious case. I cannot, however, say that I would always disqualify a politician for flirting, even of the flagrant variety, nor even necessarily for cheating. It would count against him. But our hearts lead us in strange ways, and I would not want to rule out an excellent legislator solely on the ground that he broke his marital vows. Things like self-control, and, failing that, discretion, would also enter into my assessment.