Unfortunately, with today's politicians in Washington, the saying that where there is smoke there is fire usually holds true. If it did not, then I would say that rumors should not be reported by the news media. However, given the scandalous climate in DC, we deserve more rather than less information.
No, I don't think that the media should be spreading rumors about politicians. It's one thing to publish documented facts with proof about them, and few politicians are saints. But it's quite another to start printing rubbish based on things with no backing. That's irresponsible and should not be allowed.
I don't think news media should reports rumors about anyone, be that politicians, celebrities, or regular people. We want verified facts, not rumors. If there is a rumor the media thinks would be cool to report, they should go check it out first. And if it's not true, then the shouldn't report it.
I think a big problem with United States media in general is the way that we report anything that happens, no matter the validity, merely to be the first person to the report or to get great ratings. If we focused on authenticity and reliability we would be much better off.
Rumors about politicians should not be reported by the news media. The public relies on the news for the facts and not rumors. This has notably changed in the last decade of news media. The media seems to function more these days off gossip and rumors besides actual reporting of the news.