Round manhole covers cannot fall into round manholes.

That would go for triangular covers too. Actually, it wouldn't. With an equilateral triangle, the distance between a given vertex and the center of the opposite edge is shorter than the length of each side, so it could still fall through. Of course, with other shapes of triangles, they'd fall through much more easily. -- KevinMcConnell

    Round manhole covers can easily be rolled along the ground by one person.

Good reason for wheels to be round, but many heavy semi-permanent things, like JerseyWalls?, aren't round and still work fine.

    Round manhole covers do not need to be rotated to a specific orientation to fit over the hole.

Um, yeah, so I guess square doors and windows are just a common mistake? Their orientation is fixed by their hinges and frames.