Energy released when a fiber snaps.
A carbon nanotube that is stretched to 65 GPa has a very high energy density. I have estimated that if that energy is all converted into heat, the carbon nanotube would heat up on the order of 1000K to 4000K (depending on assumptions on the Young's modulus and the heat capacity of the material).
If a thread of the space elevator ribbon breaks and a significant amount of the energy it contains is released as heat, the resulting temperature rise could be sufficient to damage the adhesives that are supposed to be holding the thread to do load redistribution, and possibly damage the interconnect. The broken thread could also zip past many interconnects before the inertia of the free end of the thread prevents the energy to be released too violently (the heat radiates away very fast). This would leave lots of long threads sticking out of the elevator ribbon, ready to get tangled on advancing climbers. Given current estimates, it would seem that there would be many breaks per square meter of ribbon per year, so there would be a lot of these threads around.
The elastic energy that gets converted into kinetic energy could also have a negative impact on the interconnects, possibly damaging them or allowing the thread to zip through.
Thermal cycling when ribbon twists.
In space, the temperature of the ribbon is governed by radiative heat transport. When the ribbon is facing the sun, it equilibrates to a temperature around 300K. When it is perpendicular to the sun, it equilibrates to a temperature around 100K (I haven't checked these numbers myself, but they are in the right ball park). Because it is so thin, the ribbon's temperature will equilibrate within a few seconds only. Therefore, if the ribbon is twisting around randomly, it will be repeatedly be cycling from hot to cold to hot. This temperature cycling could cause some severe fatigue issues as it is repeated year after year after year. In fact, just the large range of temperatures could be a problem; polymers tend to have mechanical characteristics that vary significantly with temperature. Certainly a challenge for the materials folks. The thermal expansion caused by the temperature change could also induce oscillations in the ribbon, but I think that is a lesser concern.
One broken elevator could kill all deployed elevators.
If a space elevator breaks, a number of very long pieces of ribbon result. Ones attached to the Earth will fall down (pretty harmlessly for the people on the Earth); the others will orbit the Earth going West (unless I am mixed up). These ribbons will probably have a bit of motion out of the equatorial plane (at least tens of km in amplitude), and the total length of broken ribbon is very long, so there is a very good chance that they will strike other elevators that are around (and that are very large targets). The collision itself will usually be at relatively small velocities, so it shouldn't be a problem. On the other hand, after colliding, the ribbons may rub against each other, get caught on each other resulting in ribbon damage, or increase each other's tension. It seems to me that this could severely damage or even break the elevator that is still standing.
Having multiple elevators was supposed to be insurance; it may turn out to be more like putting all your explosives in the same box.
New #1 terror target.
If the tether ever broke the people in the hotel are in the deep weeds.
oh, sorry....saw the title of the thread and it was just a natural occurrence....
Don't tell the Moslems.