Needs more tests, and random tests.

Images are broken, wrong(wikipedia was never a commercial) links.
[I'll fix them, soon]

(This last because the Test.expectError() call does not seem to handle errors as stated.)

This is actually because you didn't read the docs properly and see that Test.expectError expects a function argument. You have to wrap the call into a function.

Input validation does not add to the problem. Please just don't.

Polygons with points in clockwise order are not tested.

As with http://www.codewars.com/kata/point-in-polygon-1/

Polygons like these were not tested:

var thisPolygon = {'polygon' : [
		{'moveto' : {'x' : -5, 'y' : -5}},
		{'lineto' : {'x' : 5, 'y' : -5}},
		{'lineto' : {'x' : 0, 'y' : 0}},
		{'lineto' : {'x' : 4, 'y' : 4}},
		{'lineto' : {'x' : 3, 'y' : 1}},
		{'lineto' : {'x' : 1, 'y' : 0}},
		{'lineto' : {'x' : 5, 'y' : 0}},
		{'lineto' : {'x' : 5, 'y' : 5}},
		{'lineto' : {'x' : -5, 'y' : 5}},
		{'lineto' : {'x' : -5, 'y' : -5}},
]};

thisPoint = {'x' : 1.01, 'y' : 1};
Test.assertEquals(pointInPoly(thisPolygon, thisPoint), false, 'Point is outside the polygon');

thisPoint = {'x' : 0.99, 'y' : 1};
Test.assertEquals(pointInPoly(thisPolygon, thisPoint), true, 'Point is inside the polygon');

And I believe many solutions will fail on convex polygons like that.

(This last because the Test.expectError() call does not seem to handle errors as stated.)

Test.expectError takes a function argument, which it calls and expects an error to occur. You're probably writing something like:

Test.expectError(somefn(baddata)); // error occurs outside of Test.expectError so it can't handle it

rather than,

Test.expectError(function () {
  somefn(baddata); // error doesn't occur until Test.expectError calls this function, so it catches it
});

Note that the first way (the way that didn't work) is equivalent to this:

var result = somefn(baddata); // error occurs here
Test.expectError(result); // of course it can't get to this line, it's already halted due to the error

What's the point of saying a polygon can contain curves, if it can't really contain curves?