AccuSnap and the Intersect Snap
To select the intersection point of two elements requires you to identify both elements. AccuSnap lets you do this by simply pausing the mouse over the intersection point of the two elements, without entering tentative snap points. When the pointer is over the intersection point, the elements highlight, one solid and one dashed, and the tentative point marker displays at the intersection point. Where a number of elements intersect at a common point, you can move the pointer until the correct pair of elements highlight.
In a 3D DGN file, the two intersecting lines may be separated in the view Z direction. By default the element nearest the Active Depth of the view is highlighted as a solid line and it is on this element that the data point will be placed. That is, the new element is attached to the element highlighted as a solid line. You can control this by manually snapping to the required element first, before moving the pointer to the intersection point. That is, snap to the element to which you want the new element attached, then move the pointer to the intersection point. The first element will highlight as a solid line, and the remaining element as dashed.