This had me puzzled. On the BBC News page http://bbc.co.uk/news I found that in Firefox ESR the fonts were all showing as not anti-aliased. Other pages OK, using Waterfox and Seamonkey OK. Same on both Live ISO and installed.
I checked all my settings, using new clean profile, no matter what they were still jaggy - but just that one page!
Anyhoo, from the very dim past I remembered once upon a time it used to be necessary to run dpkg reconfigure fontconfig-config on occasions. So, I did that using default values and it worked, pages rendered correctly.
There are probably a number of reasons why, but anyway that solved the problem.
Yay! Thank you, this worked regarding the Yahoo Mail website (which for me was the only site where the font looked jagged).
By the way: the command should literally be
dpkg-reconfigure fontconfig-config