I was a bit concerned when I first heard of this.... about 5 or 6 months ago. But I'm running Fedora Core 1 (as well as several other, older RH installs going back to RH 6.1) and I'm really happy with FC1. Avaliable updaters include apt, yum, current and up2date. The community support, both on the Fedora list
and forums such as this one is excellent.
For your server, you may want to consider one of the RHEL products, especially if you consider it to be "mission critical" but if you've been using RHL products in the past without purchasing support, give Fedora a look. I don't see that it's any buggier than the previous RHL releases.
One other possibility would be to take a look at the Fedora Legacy project (google it, it's out there). They are working at providing extended support (errata and etc.) for EOL'd RHL/FC releases.