In JIRA 6.1.2 when trying to re-order a custom field when I click and hold on the grey verticle bar to move the field is added to the "remove" section at the bottom of the page. I have tried in Chrome, FireFox and IE.
Following the directions from here
Move a field: Hover over the dotted part of the field (next to the field name) and drag the field to the desired position.
Move a field to a different tab by dragging it to the name of the tab and dropping it.
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