In object mode there is a blender element attached to a particular object which appears to be a vertex, though I'm working in a large scale, so it could be a small edge or face. I don't want it there, but I cannot seem to select the item in object mode, and it disappears in edit mode.
A hard to find or select object can often be deleted from the outliner.
Here I have a cube that has all of it's vertices deleted but is still a child of another cube. In the outliner I can expand the parent to see the child, by right clicking on Cube.001 I can then select delete.
Check to see if you may have added a modifier to your object. Some modifiers, for example, the hook modifier, add empties that are used in the function of the modifier that show in object mode, but which cannot be selected in edit mode.