I hear what you're saying and you're right that WinPython & Anaconda certainly help, but the documentation is still a long way off from Mathematica in my opinion.
One thing in Python's favor though might be depth in certain categories. The machine learning stuff in Mathematica is very nice and high level if you want neural networks, but if you need PSO or GA, you'll probably have to write your own or grab someone else's notebook.
It was difficult for me to support closed-source software as I've always supported linux for this reason.
As far as ensuring accuracy of calculations, having a very large and highly technical user base over several decades helps, but I'm not sure how much this is used in theory. If a statistician publishes a paper using R, is anyone really going to check the R module source code? I bet this is a rare occurrence.