In the component editor, if the grid is set to .025 inch, and a pin moved .025 from center, then the grid set to .05 inches, the part will snap to grid .025 off.

I believe the other editors (PCB, schematic) have this same problem.

I don't understand the problem. Do you mean that the part doesn't snap to bigger grid?

Yes, but not correctly. If you place 2 parts on a small grid, and one part gets half a grid off, you can't align them if you make the grid larger. You first have to downsize the grid, line up the parts, and up-size the grid, which I hope isn't by design.

I've always assumed this to be a feature (correct me if I'm wrong!).

Basically the grid size does not specify what pins/origin snap to, but rather the minimum amount which can be moved.
I use this quite often when creating a pattern. Changing the grid-size, then moving said distance using the arrow keys. If it behaved like you expect, that would not be possible. Not sure which is best really.

I think I would personally prefer to have it stay as it is, and then have a separate function to force a component to align to the grid.

I see what you mean. I don't think it is big problem, but we will consider it with our team.