I don't know about physics, but in mathematics and theoretical computer science, there are really two problems that are not solved by arXiv:
1. We need a way to record mistakes in proofs / get an idea of the level of confidence in the proofs in papers.
2. There should be a way to collect papers of significance, to be able to get an idea of which papers are important.
Both are problems that have been solved in the past (more or less) by journals, and they are outside the scope of what arXiv is intended to provide. Nevertheless, there is still a lot of space for clever new models of open publishing, outside the traditional models. Unfortunately for the audience here, those problems are mostly social and political rather than technical (e.g., how do you break the influence of journals in academic hiring decisions).