How place and move objects with small increments

If you copy a slide object (CTRL-C, or however), you can press SHIFT-CTRL-D to duplicate it into the same location. If you copy something and then move to another slide or layer, duplicating it there should place it into the same coordinate location it was on the original slide.

For fine tuning, selecting an object and then using the cursor keys to nudge the position usually shifts objects by one pixel at a time. You can also use the Size and Position section of the Ribbon (under Format), or the associated dialog window to manually set the pixel positions. If I need to ensure exact positioning, I verify the x and y values here, or set them manually. This is especially valuable when placing new objects that default to positions (and sizes) other than what I want.

p.s.: pressing ALT while dragging an object disables the snapping to other objects and can make small drag movements easier.