Thanks for your quick response!
I just checked and all of the attributes are checked, including the shape. This is an mxd with 3 point layers. I was thinking it may be tolerance and so have been playing with that, but considering that the draw-a-polygon-and-perform-an-intersect doesn't work, either, I don't think tolerance issues will solve my problem. Any other places I can check?
EDIT: I just tested each of the 3 layers, one one of them is working properly. It is the layer that only has 2 features in it. The other 2 layers have about 2K each and derive from the same shape file (total of about 4K features). I will continue trying to inspect the differences!