There was a daily show episode years ago where the guest compared economics in a nobel prize context to monkeys throwing theses at one another.

Wish I could find that clip for you.
To me the glaring problem is precisely the lack of a scientific approach, so by definition economics cannot be a science because it is based on theories validated by abstract empirical studies (or not at all), as opposed to being derived from "first principles" - Those things that cannot be denied. For example in physics and science everything we accept (notwithstanding of course the purely theoretical stuff) starts from physical laws, eg, gravity and temperature can be measured... laws of motion... etc...
Some things in the monetary system could be defined, eg, what is a currency? what are people? Those are the fundamental starting points to a scientific theory and framework for a science. I once set out on a mission to do this and came up with a model of inflation. Go figure