The physical space elevator should not be a significant danger to non-passengers. Proposed locations are far away
from civilization, so there is little chance of an aircraft colliding with it, or any other similar disaster.
Luckily, the material that is being considered for the tether is not particularly dangerous if it was to fall.
With a weight around shrink wrap, no amount of tether falling form the sky will hurt people, animals, or infrastructure.
However, the danger of carbon nanotubes is not fully known yet. Although it is most likely not chemically reactive
and unlikely to significantly damage the environment, it is hypothesized that, like asbestos, it can be taken into
the lungs and cause long-term damage if its turned into a friable state.
It is quite possible that there could be a break in the cable. However, this does not necessarily spell disaster
for any payload currently on the tether. As discussed on the Liftport homepage, it all depends on where the break is:
"The short answer is that some payloads will fall (below the break and below 24,000 km altitude), some
will enter low orbit (below the break and between 24,000 km and GEO) and some will be tossed to high Earth
orbit (above GEO) depending on where the payloads are and where the break is. However, what happens also
depends on the reaction of the payload. In other words, what happens depends on lots of factors. Escape pods
or re-entry vehicles may be required depending on designs. "
If built with an eye towards safety, there is no reason that a space elevator cannot easily exceed our current
method of getting materials and people into orbit in safety. As highlighted by the Columbia and Challenger disasters
(not to mention the many Russian and Chinese space disasters not publicized in the Western media), getting into
and out of space is a naturally very risky operation. Slowly climbing up a rope certainly looks to be a safer and more
comfortable experience than being blasted into Earth orbit on top of a controlled explosion.
It is worth noting that there are many other safety concerns, far too many to be explored here.
Liftport, a company looking for investors on this venture, naturally has a very well laid out summary of the dangers
of building a space elevator.