[john.gersh]

There are four "snappings," and if they're all turned on, I can see how they might interfere with placing things where you want. Controlling them can be a bit confusing, though.

Grid: There are controls in the Grid inspector and in the Arrange > Grid menu. Snap to Grid sets the global feature. Align to Grid is an action on the selected objects, and can be done even when Snap to Grid is off.

Smart Guides: The other snappings are controlled in Arrange > Guides. Check or uncheck Smart Alignment Guides and Smart Distance Guides

I'm not sure what you're talking about in the Magnets paragraph. Is the problem in moving a shape's magnets themselves using the Magnet tool, or in connecting lines to to a shape? I'd have thought that magnets would always be positioned relative to their shape, rather than to grid points. Magnets do snap to positions that are multiples of 1/4 of a shape's height and width as well as to the edge of the shape.

If you're talking not about adjusting magnet positions but on line-connecting behavior, there's another, perhaps-confusing issue. If "allow connections from lines" is set on a shape (Connections Inspector) and the shape has no magnets set, then a line will connect as if it's pointing to the shape's center. I guess that's as good a guess as any if you've said that lines should connect but haven't specified the connection points.