Underwater stuff rendered as if light reflected from the water's surface also passes through the water's surface
I had a thought the other day - all that light that gets reflected off the top of the water towards the camera can't also be getting through the water and lighting up whatever's underneath it. I don't believe we're doing anything about that, so that would make the underwater stuff too bright, which would potentially go a long way towards explaining many of the confusing and surprising effects from the water shader.
The actual implementation doesn't have an obvious answer - as well as the refraction and non-refraction paths using different approaches to render underwater stuff, the light takes a whole bunch of different routes from a point or directional source via the ripples to a single point (hence caustics), and underwater shadows don't account for there being a bend at all (in fact, I can't remember whether they were ever made to work on the opposite side of the water plane to the camera in the refraction path).