It may help if you posted a screenshot of the Gerber display, and one from PCBNew showing approximately the same region.
If you have not yet heard the admonition, LISTEN CAREFULLY NOW:
ANY time you send a Gerber file to a fab house, review it with a Gerber viewer first!
I have never encountered anything like this, and I'm certain that if it was truly a bug in KiCAD, it would have been discovered, analyzed and reported by now. (I think stable version 4.0.4 is about 4 months old now.) The fact that you see the same defect in both the Gerber viewer and the 3D viewer supports the idea that the lines are truly there, not just an obscure artifact manufactured by a video driver or graphics card. With that in mind it seems that it should be visible in PCBNew.
The following comments are WAG's on my part.
Is your "Edge.Cuts" layer clean? If you had stray lines on Edge.Cuts, they will be plotted on copper layers when you generate Gerbers, unless you tell KiCAD otherwise in the "Plot" dialog.
A similar comment can be made about the "frame" (or "format border" ) of the worksheet, though this is less likely.
Did you inadvertently move a trace or graphic element when you moved a group of components?
Did you inadvertently start to draw a line or trace, then realize you had not selected the active layer you wanted? (Especially if the active layer was not visible during the drawing. After years of using EDA tools, I still occasionally start to place a line or trace, only to discover it's not going onto the layer I want it on.)