Computer Modern Roman is a shibboleth. When I used to review resumes at Google I'd give extra attention to any resume in CMR; we wanted to hire the kind of nerd who has a resume.tex. I don't like the look of the font myself and long ago switched to Postscript fonts but that's a subjective opinion.
In the true nerd spirit, shouldn't you check the pdf metadata to see if the resume was created by tex. I use TeX (well ConTeXt but not LaTeX, but that is a minor difference) for my resume, but without using CM or LM fonts. With Luatex, you can use any opentype font.
I used to do my resume in TeX (in fact an ancient resume of mine along with the plain TeX macros to format it is on CTAN), but I stopped because in most cases, my resume is getting slurped into some automated system and if it's anything other than a Word document, I end up with a lot of pain.
