What would be the obstacles to building a 6.5km space telescope besides cost? In the comments of another question on this Stack Exchange site, I talk with another user about the possibility of building an optical space telescope with a 6.5 km aperture.

Obviously, this is much larger than any rocket we have constructed, so it would need to be launched from Earth in a number of components and assembled in orbit in a similarly massive number of spacewalks, and the sheer scale of it would likely require active heat management systems to prevent heat expansion of the components from sunlight warping the mirrors or stretching the distance between the mirrors.

Are there any other obstacles that would prevent this project from being possible?
The basic issue with a large optical telescope is to keep all of the mirror in an extremely stable position relative to the rest of the mirror. Depending on the wavelength of your light you probably want to limit deviations from your perfect shape to less than about 100nm, so, you need to account for and deal with somehow any force which might act on one part of your mirror differently from another with enough force to bend the whole mirror by more than this tiny amount. At a glance, therefore you will need to deal with:


tidal forces from Earth, Moon and Sun (I think you can ignore tides from Venus and Jupiter, but I'm not certain)
Orbital perturbations arising because Earth is not spherical
temperature variations from moving in and out of Earth's shadow at different times and from sunlight and Earthlight (and maybe moonlight) hitting different parts of the structure differently
interactions of any conducting components of the mirror with Earth's magnetic field
flexing and oscillations of the structure arising from thrusts used to point the mirror


and probably a lot more that I haven't thought of.  These problems would become somewhat simpler if you put the telescope much further from the Earth, or even better much further from the Sun (say a very distant orbit around Neptune) but that would make assembling it by spacewalking impossible.