I haven't noticed any major problems myself. I few things that don't work anymore though, but did with KDE2. Aside from the desktop though, I only use KMail and KNode as full time apps. Konqueror on the web has worked OK the couple of times I have used it. Konqueror for local file operations is where I have found some options that don't seem to work anymore. I don't use the KOffice stuff, so I am unable to comment. So I would think the base KDE 3.0.1 appears to be stable.
Since GNome is based on GTK I think and KDE on QT3 now, perhaps there are some library issues. Maybe upgrade QT3 first, if available? It looks like I have QT 3.0.4 installed from the Slack 8.1 CD.