As I understand it, this is one of the main reasons that there are two detectors thousands of miles apart, in Washington and Louisiana. There will be a whole lot of false alarms at each one separately, but it's extremely unlikely that precisely matching earthquakes will occur at both locations at once. (They have other very sophisticated ways of isolating the system from outside noise, too, of course. But I don't think the experiment would be viable without the two location filter.)

As for space, the LISA project has been trying to get funding for years. (The preliminary "LISA Pathfinder" mission launched on Dec. 3, so there's finally some real progress on this: http://sci.esa.int/lisa-pathfinder/)

They want to do this in space: https://en.wikipedia.org/wiki/Evolved_Laser_Interferometer_S...

Funding is limited though, and doing it on the ground is easier to develop and maintain/troubleshoot.

> This is also the first thing that came to my mind. How do the filter noise? Or are we missing something that is not described in the article?

The mirrors are suspended from pendula: https://www.advancedligo.mit.edu/sus.html