MathJax rendering in browsers (right) is a lot blurrier than the equivalent PDF rendering in LaTeX (left).
Is this a Javascript limitation, a browser limitation, a MathJax limitation, a bug, by design, or something else? Is there any way to improve the rendering?
The quality of the font rendering has a lot to do with the browser and OS you are using. You haven't said what these are in your case, but the results look like Chrome or Firefox on Windows. Here is Safari on MacOSX:
(source: dpvc at www.math.union.edu)
and this is IE9 on Windows 7:
(source: dpvc at www.math.union.edu)
while Chrome on Windows 7 is:
(source: dpvc at www.math.union.edu)
So there are a wide range of results depending on the browser and OS in use. That is the result of different font rendering technology, and in my experience there isn't a lot to be done about it. Perhaps someone with more font experience than I can suggest a way to improve this.