So, I just got a huge thread of comments to the previous comm post, all reporting that LJlogin suddenly isn't working anymore. Alas, I can confirm it: It's not working for me, either. As several others have speculated, I suspect that when the LJ crew made some update to their code, they either changed or broke the client interface. I haven't dug up the root of the changes yet, so until LJ either fixes it or tells us how it's supposed to work now, I can't offer any estimates on my ability to make LJlogin work again or how long it'll take to do so.
Everyone cross their fingers that this is just a temporary mistake, and that they'll get it fixed quickly.
EDIT: As the link in the first comment to this post shows, LJ is aware of the problem with client authentication as well as the other notification-related problems other people have been seeing. Also, there are reports that it's working again, so hooray for that.