This is usually normal behavior or a settings issue, not a defect. On the D7000 in Live View, if Manual movie settings are enabled, the camera limits what can be adjusted and shutter speed is only available in a certain range. Also, with many Nikon DSLRs, the actual aperture stop-down may not visibly change in Live View until you take a photo or exit/restart Live View, even though the displayed f-number can still change.

If the displayed aperture value does not change at all, check for a control-setting conflict: on the D7000, custom setting f7 (Release button to use dial) can temporarily reassign the dials after certain button presses until you cancel it or half-press the shutter.

So: first check Manual movie settings, then check custom setting f7, and make sure no button is being held while turning the dial. Based on the community reports, this does not point to a faulty camera unless the aperture value never changes even after reviewing those settings.