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Have you noticed people misapplying that to galaxies? They'll claim there is no influence on a star due to the part of the disk at greater radius, and also that the mass inside that radius can be treated as a point mass. But disks are not spheres, and rings are not shells, so those simplification do not apply. I've seen this mistake many times.

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Interesting question. Given n stars/whatever at varying positions, is there always at least one point where the gravitational forces cancel out? Or is that just a solution to the simple cases of two bodies or a single body in the form of a sphere or shell?

I can't do the math to determine this more rigorously, but my intuition tells me you can do something analogous to the Hairy Ball Theorem to prove that there exists a point within the convex hull of those stars where the gravitational forces cancel out. However, as the stars move, there's no guarantee that point will remain static and stable.

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