Yep. Sometime after this interview I figured out what my Apache configuration problems were. The short version: KeepAlive, which might as well be called as TurnThisOnToBlockThisServerTotallyEveryTimeYourSiteAppearsInSocialMedia.
There's also just tossing a reverse proxy in front of your apache, it hands the problem of slow requests, bad requests, KeepComatose, etc to something lightweight that's a lot more crap-tolerant.
http://joshua.schachter.org/2008/01/proxy.html
The simpler of these (e.g. pound) take about as much time to set up as scrolling through your apache config looking for some mis-set option.
Give Nginx a spin if you can. I use 300MB VPSes running Nginx + PHP and have memory to spare to run the dropbox daemon, lightly loaded mysql, etc.