If you're looking for a rendering engine that does all of that first list right out of the box, I don't think you'll find a whole lot. Stuff like fancy lighting shaders and day/night stuff are very game/simulation specific, and most rendering engines either won't have that sort of thing built in, or the built in implementation won't meet your specific needs.
I use Ogre3D, which I wholeheartedly recommend:
open source
Ogre is open source, under the MIT license.
day/night cycles
Nothing built in, though there are a few extensions that do this sort of thing (Caelum comes to mind).
dynamic weather wind/rain/clouds/etc
Again, nothing out of the box, but there are a number of extensions that do something like this (again, Caelum, and also SkyX).
wet surfaces (surfaces look wet during rain)
You'll have to write a shader for it, but it is possible (I have achieved such an effect in the past with Ogre).
realistic water
There is a plugin or two for this (Hydrax is rather pretty), and the 'Fresnel' SDK sample shows off a simple refraction/reflection water shader (and there's another sample or two devoted to water effects).
large terrains with the ability to define "roads"
No roads, but Ogre recently got a new terrain system that is very nice.
seamless exterior and interior
Ogre has a few different plugins for portal connected zones, BSP's etc, so it should support whatever you need.
forests (lots of trees, clutter, etc)**
Ogre has some batching capabilities built in, and the Paged Geometry addon is supposedly quite nice.
realistic lighting (ie. light from a fire/candle flickers)**
Aside from some example shaders included with the samples there aren't any built-in lighting shaders, but the material/shader system makes it very easy to get a lighting shader up and running.
Overall, Ogre is capable of all of that, and has a very robust material/shader system, but you will have to write the shaders for a lot of the effects yourself (and this is true of most other rendering engines, you can't really make one-size-fits-all solutions for a lot of these effects).
