And, in my eight or so years of experience using Mac OS X's DU for cloning, up to Snow Leopard and now with Lion using CCC, cloning from the boot volume works just peachy fine. And I never bother to close down the internet connection either. Unlike Tacit, I don't bother to close down all the apps I've just been using. So what if Text Edit is open and so is Safari? Makes no difference.
With those two programs in particular, you're unlikely to have problems. A TextEdit file that's open isn't held open for writing on the disk; the only way you'll have an issue is if you save that file at the exact moment it's being cloned, which is unlikely. Having Safari open while you clone may result in the Safari cache files on the clone being a bit scrambled, but that's no big deal.
Other programs are more problematic. Some programs, including Mail and iPhoto, use SQLite databases. Carbon Copy Cloner doesn't know how to deal with these in a coherent way; it just treats them as files. If you're cloning your Mail database while new email is arriving, or cloning your iPhoto database while you are importing, tagging, rearranging, rating, scanning for faces, or sorting photos, you may end up with a clone that has a scrambled database. This isn't too big a problem in Mail--there are ways to force it to rebuild mailbox indexes--but in iPhoto, your library may be unreadable and have to be rebuilt. I've seen this happen. Rebuilding an iPhoto library is not easy, and you lose all your album names, ratings, tags, and faces.
I don't recall seeing an 'RHV' back at the MacFixIt forums, but there were frequent threads there about unbootable clones. Same at macosxhints. Or —if the clones were bootable —the other fun thing that happened is that utilities like DU and DW would refuse to repair the original while booted from the clone.
I haven't seen that problem, and I'm a bit mystified how it could happen. The only way I can see for such a thing to happen is if the clone were still referencing files on the original, via aliases or symlinks or some other mechanism, and as a result the original drive still had open files. That's a problem that's not necessarily related to cloning
per se.
Certainly I've never experienced that problem. I've been using tools like CCC to clone active boot volumes for many years, and have probably at this point done it literally thousands of times (not only on my own systems but on clients' systems as well) without problem.
