I heard that today as well, and am happy that they managed to salvage the mission.
For your other questions:
Well, the Earth's magnetic field doesn't work quite that way. For one, the field lines tend to be tangential to the surface of the earth for almost all of it's surface. This would require something a little more exotic than simply a strong electromagnet above the ground.
The other thing is that the field strength drops off as 1/(distance)^2. So the power requirements would be huge to beat gravity, and even then you'd have a coil/generator to mass ratio with a high enough efficiency so that you could lift the entire apparatus. Superconductors help though

.
Now, using the Earth's ionosphere, we do similar things in space using the E-field instead (the E-filed is cooler than the H-field anyway

). For low orbit, tether systems are employed to essentially induce charge/potential difference on one end of the tether, causing a net force in a certain direction depending on that charge. Currently we use such a system to control and hasten the decay of slowly decaying orbits. Basically, it acts as a sort of EM "anchor."
However, if we were to actually build a space elevator, I think that electromagnetic locks on Earth would be an excellent choice for anchoring it down. Rather than some sort of mechanical anchor to bedrock or something, a field controlled anchor could allow for more flex or slack, etc... easier. The only problem is that it would require mechanical failsafes.... But there are actually intellegent scientists, researchers, and engineers that meet to talk about the serious viability of a space elevator...
Another option for getting into space: inductive launching. Like a long EM rail gun with a barrel burrowed through miles of mountains, and shoots the payload out into space... maybe not a good idea for manned flight, but eventualy for resource delivery it could be possible...