The things that obviously should have tests have tests. That means most of the things that touch money on our Careers product, and easily unit-testable features on the Core end (things with known inputs, e.g. flagging, our new top bar, etc), for most other things we just do a functionality test by hand and push it to our incubating site (formerly meta.stackoverflow, now meta.stackexchange).
You can look at reported bugs here: http://meta.stackexchange.com/questions/tagged/bug -- it's pretty frequent, at least one every couple of hours or so. The last commit in our "Tests" project was 14 days ago, where as the last commit in the code base was 4 minutes ago.
Indeed, they seem to have achieved what many have said is literally not possible.
Also, some might remember when they had Uncle Bob on the podcast, the topic being unit testing, and iirc Bob preaching the gospel (~ you must write plentiful unit tests, or else) and Jeff and Joel (especially) more or less saying they don't quite get why.
(Am I remembering this story correctly? I swear that's how I remember it.)
You can look at reported bugs here: http://meta.stackexchange.com/questions/tagged/bug -- it's pretty frequent, at least one every couple of hours or so. The last commit in our "Tests" project was 14 days ago, where as the last commit in the code base was 4 minutes ago.