Can a motor's movement be improved to any arbitrary resolution?
It is possible to microstep stepper motors.  If you get the correct drivers, they can interpolate the steps into a large number of subdivisions.  I have seen drivers that can do 256 microsteps per step.  With 1.4 degrees per step a pretty standard figure, you only need ~10 microsteps per step to get 0.15 degrees per microstep.  8 microsteps would give you 0.175 degrees per step, and you can get all-in-one microstepping driver chips from Allegro that can do up to 8 microsteps per step.  I used the Allegro 3977 a few years ago for a project.  16 or 32 microsteps per step would give you 0.0875 or 0.04375 degrees per step, which should be more than sufficient.