I like Devdattas' answer but if you don't know or understand python you can select individual records of an overlapping 'heap' (usually sitting upon Null Island indicating there was a problem with importing the records) with the attribute table by clicking on the row number.
From there you can edit the coordinates manually by right clicking with the edit tool active and select 'Edit Vertices' from the context menu, this should open your Sketch Properties:
Which you can use to modify your X, Y, Z and/or M values - even for a point, but like I said in my comment this is tedious to do more than a few times; I almost always go back a step and correct the records prior to re-importing.
This handy utility is also good for checking/finding small holes in very large polygons: go to the next part in the list, click on the top row to select the part:
Right click and either Zoom To or Pan To the hole, from here you can also delete the whole part to remove a hole or external polygon. You can also tell if the points do not have part 0 right at the top of the list that there is no holes in this polygon.