Lisa, I think you have two different issues. One is the visual aspect. I think ArcMap lets you zoom in past 1:1 but in my experience beyond that what you see is not what you get. The other is the topological/snapping aspect. If you are attempting to move a vertice of one polygon to snap to a line of an abutting polygon with the idea of having their edges be perfect coincident, there may be a problem because of the precision. That vertice has to "snap" to some underlying grid and that point may not be "on" the line. I think to have perfectly coincident shared boundaries in shapefiles and feature classes you have to have vertices in the same place. Having said that the difference is probably so small you wouldn't notice it, and you probably can't see it due to the visual limitations. And even if you could, as one of my coworkers said, you can fix errors or you can make your lines thicker and/or change your scale.
If you create a topology and verify it I think a matching vertice will be added along the line of the abutting polygon. Or you could clean your layer after editing. Introducing a vertice along a line by either approach may cause it to "jump" in comparison to the backup dataset without that vertice, however. Or you could convert your polygons to lines and points, clean the lines, and from then on edit them and build polygons using the lines and points, the points providing the attributes. Then a single line is used as the boundary for abutting polygons much like a coverage works.