Ask a Physicist
How can one know that the length of one arm is exactly 4km (or so)?
Actually, what the interferometer measures is the difference between the lengths of the two arms. They're not both exactly 4km long in the absence of a gravitational wave, and that doesn't hurt the sensitivity at all.
LIGO doesn't even really measure the length difference so much as changes in the length difference. And it's much more sensitive to changes on some timescales than on others. For example, if you shake it at 100 Hz (cycles per second), which is what many pulsars do, it is quite sensitive to that particular shaking. If you shake it at 10 Hz or 10,000 Hz, it's much less sensitive.
At high frequencies you see fluctuations in the light that drown out your sensitivity to gravitational waves anyway. These are basically quantum mechanical fluctuations, which are normally equally small at all frequencies. But LIGO is set up so that they get fed back through several mirrors and become worse at high frequencies, which is the price of making them better around 100 Hz.
At low frequencies, any signal gets drowned out by seismic noise (ground rattling from earthquakes, cars, footsteps, ocean waves hitting the coast hundreds of miles away, you name it). It is possible to put in various insulating mechanisms. They are there, and they are incredibly good (LIGO inspired the cutting edge here). But as you get down toward 10Hz the Earth just gets too noisy no matter what you do; thus the plans for LISA (a space-based LIGO).