Great post!
This phenomenon was observed as a red-shift of a galaxy's spectrum. This red-shift appeared to be larger for faint, presumably further, galaxies. Hence, the farther a galaxy, the faster it is receding from Earth.
Would that mean that at some point, a visible star/galaxy's light would be so red-shifted that it moves out of the visible spectrum? So basically, would the night sky be darker for the naked eye in the future?
Yes, that can happen. Frightening thought that eventually in the far far far future it is possible that we will have no stars. :(