Tosh.0 is completely inoffensive, because it is made for the sake of comedy, not to hurt or offend people. People have made these videos, and sometimes have sent them in themselves. If they didn't want to be offended, why would they put a video of themselves out there for the entire world to see?
Saying something is in the name of humor is not a blanket that magically makes it acceptable to say. We must remember that not everyone has a sense of humor, and in reference to those who do, theirs is not always uniform. While I personally believe that Tosh.0 is a hilarious show that plays on the stereotypes society has created, I am just one person and while I may not take offense to it, others will and do. Regardless of its purpose to be humorous, that humor can be taken out of context.
I do agree that something being in the name of comedy isn't a blanket that makes it better. But the people who have put the videos up on the internet put them there for other people to enjoy. When Tosh.0 wants to use a clip, they get the consent of the person who created it. Someone who watches it, knowing that they might be offended, are taking the risk. They made the choice. These comments made on the videos were made to make people laugh. If they do not make you laugh, that is your problem.
Those who send in their videos may not be offended, but those who watch the show out of context are, in that sense it is offensive, but even when the show is taken in full context, it is still possible for people to get offended. Daniel Tosh, the host of the show has had to apologize for a joke before. The joke was about rape, he said, "Wouldn't it be funny if that girl got raped by like, 5 guys right now". If that isn't offensive, I don't know what is.