By the way, on the topic of why it is so far out there...
For the rest of us, you might at first blush think that they would put it in low earth orbit like Hubble, where they can get to it. Several problems with that idea - even in low earth orbit, with the shuttle retired, we have, right now, no way of getting to it with any significant repair capability. Soyuz could get to it in really low orbit like the space station, but has no real capability for capturing something like NGST/Webb or carrying repair parts, grappling arms, etc.
But the big reasons are that in low earth orbit, you have A LOT of thermal input from the earth. This is called albedo heating, heating from reflected and radiated heat from the earth albedo.
The earth is ~70 degrees, and the background of space is -450 degrees. In low earth orbit, having half the sphere of the sky filled up with a nice warm 70 degree earth imparts tremendous heat to the telescope. Since the telescope sees in infrared frequencies (heat), this is a huge noise input in the band they are looking that has to be dealt with. Of course, it also blocks half the potential targets , and may leave only 45 minutes of uninterrupted observation time if the target is in not perpendicular to the orbit plane. Additionally, if the telescope is pointing in one inertial direction, the heat input comes from different directions at pretty high frequency, causing thermal distortion of the telescope mirror that has to be dealt with.
Putting it out at the L2 Lagrange point, a million miles away, the earth is just a tiny speck, so no real heat input and no varying directional heat inputs. This makes it much more stable. The earth is not consequentially interfereing with the telescope field of view, so it can stare in one direction without having to consider where in the orbit it is. But mostly, it is just cold - which means, with the extraordinary effort put into the heat shields to block the sun, they can "run the telescope without any active cooling system". It stays cold enough even for an infrared mission without having to carry cryogenic coolants, that inevitably run out. This telescope's predecessor , SIRTF (built by my Denver colleagues), ran for 6 years, when it ran out of liquid helium coolant, did a reduced mission for a while, and then was deactivated. NGST/Webb does not require that, so it can last indefinitely (presumably until the stationkeeping propellant runs out).
Putting at a Lagrange point means that there is no net secular acceleration. This happens because the various gravitational forces and centrifugal force happen to balance each other at these points. There are 5 of them:
https://en.wikipedia.org/wiki/Lagrange_point NGST/Webb is going to point 2, that it, it will stay out beyond earth's orbit around the sun, and you will be able to draw a straight line from the sun to the earth to the point. It won't stay there without some small effort to push it around and so will require some on-board propulsion to stop it once it gets there and then to nudge it around to stay, but it does not have to push against some force, because the net force is zero.
As noted above, these guys have really thought all this out and definitely know what they are doing. I forget what our proposal for this mission was, I am sure it was credible. But Northrop-Grumman are highly competent and have a lot of experience with the sort of deployable structures dating back the deployable, moderately-large mesh antennas on the FLTSAT program dating to the early 70's. I have worked with various TRW/NG engineers as our subcontractors and over the years and on the engineering level, they are wonderful to work with, peers of equal capability.
Having said all that, a mission like this is generally designed to have a probability of success around 70% - because trying to get 80% is disproportionately expensive. The 70% then flows down to thousands of elements, all of which must have much greater than 70% chance of making it for the whole mission. Strings of these 99.7% or so probabilities are multiplied together to get the 70%.
There is usually a lot of hidden conservatism, but be prepared for and aware of the chance that something *could* go wrong. That wouldn't make the people involved incompetent or lackadaisical, it means that doing these missions is very difficult and complex, and very unforgiving of even a single mistake.
Brett