There are several versions of "the default roman font". There is the bluesky computer modern (cmr), the newer but flawed CM-Super, and the latest latin modern (lmodern).
Your document seems to use latin modern.
See this link for test google documents that I produced with pdftex using each of these 3 fonts. Your opinion may be different, but to my mind it's pretty clear that bluesky computer modern looks the best, cm-super is the worst, and lmodern is in between.
My guess is that google docs pays attention to the hinting in the fonts when converting the files: bluesky is professionally hinted, lmodern is a little hinted but it's not a priority for the project, cm-super is not hinted at all. It may be that google docs leaves the font rendering to the browser, so the results might depend on which browser/OS you are using to access google docs.
Anyway, out of these 3 fonts, my advice would be to use cmr. However, this has some downsides when it comes to writing languages with many accented characters (words with accents cannot hyphenate properly: see this FAQ answer), which you can partially avoid by the use of virtual fonts (in LaTeX you can achieve this with \usepackage{ae}
, and presumably there is a ConTeXt equivalent) (see this FAQ answer), although this will mess with copying/pasting and searching for text containing accents.
Your google doc looks somewhat worse than the lmodern version I generated. It's possible you are using an older version of the font (it's still under active development).
Really, the best way to solve all these problems would be to use a different font entirely. For example, I loaded a version of the test document using MinionPro. See what you think. As @patrick commented, all versions of computer modern are well known to be non-ideal for low-resolution rendering, and there even certain fonts that are specifically designed to excel in such a role.