The Apache server is being a dick. It keeps dying with unkillable zombie processes; these don't serve data, but they do keep their hold on port 80. The only workaround is to reboot the server. This is, of course, ridiculous. I've put a ticket in with Linode. Anyone got ideas? It's just the standard Ubuntu apache2 package.
Update: Apache was causing kernel oopses. (Things that make you go "wtf.") Linode suggest using kernel 3.9-linode instead of 2.6-linode (the default for Ubuntu 10.04, which our box runs on). We'll see how that goes next reboot. Might even fix the white-screening blog too.