It looks like those vertices are weighted to a different joint than the one you are manipulating. Select the joint. Click under [Animation] Deform > Edit Membership Tool. The vertices turn yellow, I believe, if they are being affected by the selected joint. If they are a different color, they are being affected by an unselected joint. Hold Shift to Add vertices to the selected joint. Hold Control to Remove. If not that, perhaps the weight is down to 0 so it's not moving when it should.