I've had this issue since last year, and have exited the program / rebooted my computer many times during this period. I can't remember when it started, I mostly just ignored and worked around it. I've worked out it only happens in certain circumstances.
To replicate the issue:
1. Have Evernote windowed
2. Click to annotate, the annotate window is fine.
3. Go full screen. As it goes full screen it's like that part of the window (the border around the edge) just doesn't go with it and I get left with what I call the ghost window, which I guess is just an element of the window