I think the question should be rewritten along the lines of "how did the strengths/weaknesses of internet/web browsers/etc. influence the design and implementation of Javascript?" -- in which case, I will delete my post -- because most of the question is irrelevant/wrong/cherry-picked examples that don't really show indicate much about Javascript's design.  

By learning more about Javascript -- especially using it to implement some applications -- you will find out that your points are really just traps for the unwary, but become non-issues for more experienced Javascript developers.  Understanding and taking advantage of Javascript's strengths, including lexical scoping, closures, higher-order functions, function literals turns out to be more important than getting tripped up by any of the weaknesses you mentioned.

The only interesting sub-question is:

> JavaScript has a prototype-based OOP system; most other modern languages have an inheritance-based one

I suspect this has something to do with memory limitations, but I can't find a reference for that.  In addition, as @jozefg mentioned, there are other languages with prototype systems; it has different strengths/weaknesses than "mainstream" inheritance.  Prototype-based object systems have their own rich history that you should learn about before dismissing them as mistakes.

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> However, many tasks that are easy to accomplish in other modern languages are difficult or puzzling in JavaScript

Pick any language, and pose the reverse question -- how many tasks that are easy to accomplish in Javascript are difficult or puzzling in other languages?  What does the answer say about those other languages?  (IMHO, not much -- it's always easy to cherry-pick examples, but much harder to show how those examples prevent people from getting work done)

> JavaScript has such a weird typing system that it doesn't fall into any of the standard categories (plenty of examples on WTFJS)

What is weird about it?  It's definitely not the only language that's dynamically-typed; neither is it the only one that allows coercions.  Perhaps the *number* of coercions and some unexpected behavior in certain corner cases are distracting you.

> JavaScript is extremely lenient in how it parses the syntax (semicolons are optional etc.)

How so?  Do you have any other examples of leniency?  FWIW, semicolons are optional *sometimes*; it's actually well-specified and therefore not what I would "lenient".

If this is a problem for you, use a [linter](http://www.jshint.com/).

> From a developer's point of view, most of these design decisions make developing in JavaScript harder. 

How so?  Can you provide examples?  This is very subjective.

> Conceptually, the JavaScript language seems one step behind Java, and two steps behind Python and Ruby.

How so?  Can you provide examples?  This is very subjective.

> What reasoning is behind those seemingly random design decisions?

Why do they seem random?