With the addition of its final set of solar panels, the international space station is slated to become the second brightest object in the night sky--brighter than Venus.  Now, admittedly the ISS is the size of a football field, but it's also three hundred kilometers away from the Earth directly above the plane of its orbit--but much further away for most of the people who see it.  Thousands of kilometers, for most of us.

Consider this:  on any given night, you can look up (if you're not in a city that already drowns the stars) and see satellites.  They're hundreds of kilometers away, and the biggest are no larger than a compact car--yet you can see them.  Most are the size of a barrel, but perfectly visible.

Consider Bradley Edwards' ribbon design for the space elevator cable.  This would be a meter or two wide and curved, so that it is effectively visible from all angles.  So it's about the width of a barrel, but infinitely longer.  Its reflective surface over one kilometer's distance would be at least as great as the ISS; but please multiply that light output by 35,000 because that's how many kilometers long it would have to be.  A Hoytether (open meshwork) design would presumably reflect less, but how much less?

You could paint the ribbon black.  Then again, how much would a coating weigh that had to cover 1 meter x 35 million meters of area?  The black coating would heat the cable because the sun is so intense in orbit, so you wouldn't want it to be totally absorptive.  But here's the thing:

The moon is black.

Actually, overall the moon's surface is about the shade of an asphalt highway. It absorbs almost all the light that hits it.  The moon appears pearly white to us only because of the tiny fraction of light that's reflected off the lunar blacktop.  So even a mostly-black ribbon would look brilliantly white to us on the ground.

As if all this were not enough, the only practical means of powering the climber cars (which would be visible too) appears to be multi-megawatt lasers, aimed at solar cell arrays on the climbers.  As Wikipedia puts it:

The proposed method is laser power beaming, using megawatt powered free electron or solid state lasers in combination with adaptive mirrors approximately 10 m wide and a photovoltaic array on the climber tuned to the laser frequency for efficiency.

So, the climbers are in the cross-hairs of, essentially, a set of a huge spotlights.  Maybe you could use infrared or ultraviolet lasers, but if not, then even for the most efficient solar cells (40% or thereabouts) 60% of the laser light will be absorbed or reflected.  Add to that light from the sun reflecting off the (presumably large) collectors, and you get something fiercely bright climbing the already bright cable.

This issue doesn't just affect the space elevator, by the way.  It's also relevant to any substantial effort to place solar power satellites at geosynchronous orbit.  Their immense surface area would pretty much guarantee that they'd shed a vast amount of light on the Earth.

But why should we care?  Here again we can refer to Wikipedia, in its entry on light pollution:

Life exists with natural patterns of light and dark, so disruption of those patterns influences many aspects of animal behavior.  Light pollution can confuse animal navigation, alter competitive interactions, change predator-prey relations, and influence animal physiology.

...Studies suggest that light pollution around lakes prevents zooplankton, such as Daphnia, from eating surface algae, helping cause algal blooms that can kill off the lakes' plants and lower water quality.

Lots of other life forms are affect--everything from birds to frogs.  It doesn't take very much light to have a big effect. So, in the absence of any direct physical effects, the space elevator would still have a large, if not catastrophic, ecological impact.

I wish this weren't true.  I'm a big fan of the elevator, and an even bigger fan of solar power satellites.  But the devil, as they say, is in the details.  If these structures cause the amount of light pollution I'm suggesting, then they are very far from being green options for energy and transport--regardless of how much carbon they may offset.