I've been using Godot 3.0 since the beginning of May, working on FNAF:Purgatory 2.
As time has gone on, it's become more and more stable, while bugs are disappearing. I still have to work around the new Audio engine, and a few features in material don't work on animated meshes, but I was expecting to work around some quirks.
Back in May, Godot 3 has some seriously annoying bugs (like reimporting everything whenever something changed), but now it's pretty easy to use.
I would say Godot 3 is fairly stable now. The past couple of weeks have really ironed out a lot of the most annoying/breaking bugs. There are still some little things, but nothing that would (seriously) get in the way of development.
I wouldn't recommend starting a huge project, but small/medium projects shouldn't be an issue. You should be prepared to work around some unexpected behavior and bugs at times though. Keeping up with Juan's twitter helps a lot, so you know how some of the new features are supposed to be used, along with reading through the Github commits every now and then (just a quick browse through generally works).
I've been working mostly with the 3D side though, so I'm not sure what the current stability on the 2D side is. Godot 2.1 is already great at 2D so I imagine it is mostly the same B)
And as a bonus, as more people use Godot 3, more bugs get reported, which in turn makes Godot 3 more stable.
(I'm using the Linux version. The Windows and Mac versions may be more/less stable)