The concept of "Science 2.0" was introduced almost a decade ago to describe the new generation of online-based tools for researchers allowing easier data sharing, collaboration and publishing. Although technically sound, the concept still does not work as expected. Here we provide a systematic line of arguments to modify the concept of Science 2.0, making it more consistent with the spirit and traditions of science and Internet. Our first correction to the Science 2.0 paradigm concerns the "open access" publication models charging fees to the authors. As discussed elsewhere, we show that the monopoly of such publishing models increases biases and inequalities in the representation of scientific ideas based on the author’s income. Our second correction concerns post-publication comments online, which are all essentially nonanonymous in the current Science 2.0 paradigm. We conclude that scientific postpublication discussions require special anonymization systems. We further analyze the reasons of the failure of the current post-publication peer-review models and suggest what needs to be changed in Science 3.0 to convert Internet into a large "journal club".