derng wrote:
What nutrients if any are lost in water used to soak dried beans if that
water is drained off and fresh water is then used to cook the beans?

Nothing you should worry about.

My
understanding is that this hydrates the beans and makes them more digestible
for some people.

Hydration, yes. Digestibility is a separate issue. Soaking in and of
itself is meaningless in terms of flatulence unless the beans are cooked
sufficiently. Another factor of digestibility is frequency of
consumption; people usually adjust to foods, so eating beans often will
cause less trouble over the long run. Another factor is enzymes, whether
your body produces enough or you add some in the form of foods (e.g.,
eating papaya with beans) or supplements (e.g., Beano). The herb epazote
is also considered helpful in reducing flatulence. Epazote is available
at Mexican groceries, and more grocery stores are carrying it as our
population changes.

Is it starch that is removed that relates to digestibility?

The "offensive" starches are called oligosaccharides. Traditional
soaking or the "fast soak" method of boiling for two minutes and then
letting soak for a few hours or overnight helps to release
oligosaccharides. Changing the soaking water is essential in the process.

That said, I often slow cook or pressure cook my beans *without*
soaking. They don't cause any more "problems" than soaked beans in my
experience, but I often use epazote. The key to whatever method you use
is to make sure the beans are cooked until soft; avoid adding any kind
of acidic ingredient (e.g., tomatoes, lime or lemon, vinegar, salsa,
etc.) until the beans are already soft since acid stops beans from
softening. Any undercooked bean is going to wreak havoc on your body
(and friends and lovers and neighbors).

Are any nutrients lost as well?

Not enough to worry about.