I use Neovim as my daily editor, it definitely has it's quirks over Vim (sometimes it takes over 10 seconds to write to certain files, locking up Neovim and there are some bugs with the fuzzy finder I use that cause file corruption that aren't present in Vim) but on the whole it's pretty stable. Haven't encountered any issues yet that are more than a minor annoyance.
It's a third party plugin, it's definitely a Neovim issue because the file corruption doesn't happen with Vim. No idea why it happens. I'm fine living with it because I just check the file back out if it corrupts it. It's only an issue when opening a new file so it doesn't cause work to be lost.
I've been trying it for roughly the last month. I have run into a few quirks, for example it uses non-blocking i/o for things with libuv (for stdin), which can interfere with parent processes that expect blocking i/o. If you file a bug report, the issue usually gets fixed quickly.
I've kept vim installed as a fallback so I can easily use vim if I run into anything that is a show-stopper, at least until it's fixed in nvim. I still plan on submitting patches to both for the foreseeable future though.
I use it with true color support enabled, and a terminal that supports true color, and a patched version of tmux that supports true color, and finally all color schemes render as they do in gvim!
yeah, there is a good chance you'll not run into problems. however new, serious bug reports come in frequently. for example a lot of people have been seeing segfaults, and nobody seems to know where to look.
Although Neovim's codebase is significantly cleaner than vim's, its still a far cry from what I would call good.
Been using it daily for several months now, haven't had much trouble with it. Worked seamlessly with over half a decade of accumulated vim plugins and config modifications.
Is it ready to download and run now with all the features?
No. Although some features are a work in progress, Neovim isn't at a stable point. Using Neovim should be done with caution as things may change.
This warning is why I haven't yet tried switching over. Are they just being overly-cautious?
[1]: http://neovim.io