Thank you for your post.
This issue occurs on both Mac OS X and Windows. In essence, if you remove the right border, the arrow for fields formatted as either Pop-up menu or Drop-down list will disappear.
Our Development and Testing departments are aware of this issue, and I have attached your post to the original report. When more information becomes available, I will let you know.
Not a huge problem, just an annoyance. For my scenario, I just changed the border color to the fill color of the field to match and the arrow appeared fine.