I shot a pano sequence inside a cathedral recently. Had a lens/camera combo that I had never bothered to check for nodal point, so I just rotated about the tripod screw on the body. Looks fine with objects at appreciable distance, but I cant get the nearby pews to stitch well at all. So in that case, not considering nodal point ruined a really, really nice pano shot.
Depending on the exact scene layout, maybe something is salvageable, but it will probably take a significant manual editing job to pull it off.
As I said earlier, one can either minimize parallax errors in the foreground, or in the background, but not both at the same time. So you can do one stitching operation, while only selecting background features to place the control points on. Then do another stitching operation based on only control points that are around the distance where the initial stitch started showing issues. Then another for a bit shorter distance, and so on. Then do a new stitching operation on all these intermediates, making sure that each image pair has control points at the transition zone between two optimized distances, while probably zeroing the distortion parameters since the distortions were already removed. That would basically only translate and magnify the various layers into optimal position.
In all these operations, also try a good blending program, such as SmartBlend, because it may find a better transition blend between the layers.
This will require a very good Panostitching application (e.g. PTGUI, or Hugin) that allows lots of manual control. Photoshop is probably not able to do what's needed, unless in addition you apply manual masks to each tile that needs to be aligned, prior to the varoius stitching operation runs. That would add even more manual effort.
Even then, there is no guarantee for success. But if time and effort are not an issue, it may be worth an attempt. This obviously is not something one wants to do when time is of the essence, like having to meet a deadline for a client (who is also not likely willing to pay for your wasted time).
Yes, or something sturdier for heavier cameras, to reduce vibration blur. Usually, the optimal No-Parallax settings will result in a center of mass of camera/lens combination that is significantly offset from the center of the tripod, so vibrations may become magnified rather than damped. Also, not using the multi-row setup when a single row setup is sufficient, may help to get lower vibration risk.