A couple questions that might help me to reproduce. Can reproduce this with any data? Do you move multiple vertices at the same time? Do you drag to change the position of the vertices? Do you ever double click to start the edit vertices mode? or to finish the sketch?
This has cropped up again and again since I posted this.. it's such a complete mystery and such a headache that I'm very close to closing ArcMap for good on this project and just doing everything in Illustrator.
Here's an egregious example of how messed up things are:
1. A polygon that I have attempted to cut is selected using the Attribute Table. It shows all the vertices. [ATTACH=CONFIG]15330[/ATTACH]
2. I select Edit Vertices and it displays the vertices that can be edited. What about the vertices that are selected but not editable?! Where do these exist? Do they exist? I can't trace to them, select them, or edit them, but they show up when I select the polygon using the attribute table, and they are displayed. WHAT IS GOING ON? [ATTACH=CONFIG]15331[/ATTACH]