Twitter doesn't cause problems, people cause problems.
The problem with Twitter is that it is designed for quick spontaneous comments and people forget that they are broadcasting to the whole World with it. People have always been saying stupid things like the above to each other. The difference is that, in the past, it would only be a few friends or some drinking buddies in the pub that would here them. Twitter lets you broadcast your unedited stupidity (which we all have, let's be honest) to the whole World.
The other problem is that the media treats Twitter comments seriously.