Of course, there is no direct evidence of dark matter. That is, it is, by definition, impossible to observe directly. However, many "anomalies" are resolved by hypothesizing the existence of additional mass. It seems pretty simple to me. It's not just "well, i suppose the equations would work if we add mass." It's that many aspects of observation in cosmology are directly explained by stipulating that additional mass does exist.
My point is, the theorization of dark matter is absolutely not arbitrary. There are many good reasons to believe that dark matter exists. So saying that our understanding of the laws of physics is flawed is just misleading. You say that just because it is very facilitative to hypothesize dark matter, we must totally revise the known laws, and I absolutely disagree. It makes much more sense to revise our understanding of the makeup of the universe (which is based on very difficult measurements and observations) than to revise our understanding of the fundamental laws (which are based on empirical observation of experiments).
Of course, the one big assumption we must make is that the laws of physics are consistent throughout the universe, but it is an assumption that is necessary in order to attempt to draw any conclusions at all.