As detailed in the Swing Arm Disassembly page, the Omni Swing Arm flexes when you handle the Faceting Head.
This flex can be reduced but not eliminated by tightening the Swing Arm mounting nut underneath the Swing Arm. However tightning it does not eliminate all of the flex and can make it very difficult to move the Swing Arm.
As these photos show, the Omni relies upon two plastic disks to act as a bearing between the Swing Arm and the Base Plate. I believe the flex is inherent to using a compressible plastic for this bearing.
My plan is to replace the plastic disks with brass sheeting of the same thickness. This will still provide an incompressible bearing which should resolve this issue. I will post photos of my modifications in the Omni Modifications section.
I have a report and photos from one Omni owner that his Swing Arm had a sheet of roughly-cut sheet rubber (similar to an inner tube) and a sheet of plastic as a bearing. Obviously he had significant Swing Arm flexing problems. He replaced these with sheet copper and is happier with the results.