Hi Guenther. I finally had some time to look at the sketches and features in my drawing, and check for the type of elements you mentioned. There are no Swipe features in my drawing, and there are no features that taper. All features in my drawing are joined-body extrusions, or body-cut extrusions. However, I did discover there were some features that had negative values.
I therefore then created a completely new drawing to see if I could reproduce the issue I was having (what I'm calling a MOAM) by using a negative value extrusion to create the first-of-four (i.e. original) feature; then mirror it to create the 2nd feature; and then mirror these two to create the 3rd and 4rth (quadrilaterally symmetric) features. And... voila, the Surface Body appeared on the Browser's Bodies branch; and as before, if I roll the history marker all the way to the very start –which would normally clear the screen completely– the MOAM ghost remains on display. The attached f3d file, 'MOAM Sample 01 v2' shows this.
Obviously, at that point I wondered if I could get a MOAM by not using a negative-value feature. To do that I moved the sketch elements that I was using to create the original extruded feature to a position that allowed using a positive value, instead of a negative one, to create the same feature. Surprisingly, this also resulted in a MOAM. The attached 'MOAM Sample 01 v4' shows this. So, it appears that features that use negative values are not the cause of this behavior.
At this point, I felt my original suspicion –that this problem is particular to 3D Sketches– might be correct. To further check this, I created another similar drawing that uses 2D Sketches only to achieve similar features, and tried to reproduce the MOAM behavior I've described. In this case, the twice mirrored features appeared as they should, and produced no MOAMs. This seems to confirm that the problem is confined to twice-mirrored features originally produced with 3D Sketches; and by the way, the 3D Sketch has to have some level of complexity. It can't just be a simple 3D Sketch with a couple of elements.
Given all this, I concluded that if I wanted do be able to use 3D Sketches to produce mirrored features with quadrilateral symmetry, I needed a workaround where I can mirror features once, but not re-mirror already-mirrored features. Fortunately, it turns out this can be done easily enough by first creating a 'mirrored sketch' of the sketch that was used to create the original feature. Then use that new mirrored sketch to extrude a 2nd 'mirrored' feature (the feature that will end up being what would have been the twice-mirrored feature, and always occupies a counter-corner location from the original feature), and then mirror those two features –as you normally would– to get the 3rd and 4rth mirrored features. In my case I did this by first copying the elements used in the original 3D Sketch to create the original feature; then created a new sketch on a body face that mirrored the face where the original sketch was created; and then pasted the copied sketch elements on that new sketch. I then had two 'mirroring' sketches I could use to create two features (via extrusion). Once those two features were in place I then only had to mirror once to get my 3rd and 4rth features.
If a mirrored face on which to create the new 'mirroring' sketch doesn't exist, the copied elements necessary to extrude the first feature can be pasted back anywhere in the original sketch, then rotated 180° using MOVE/COPY (to 'invert' them as a mirror would); and then moved to the proper position by doing a Point to Point MOVE/COPY. You can then use those new inverted sketch elements to create your new second feature through extrusion, and then finally mirror those two features –as you normally would– to get the 3rd and 4rth features! I would imagine this process can be tweaked as needed, all with the aim of efficiently creating features with quadrilateral symmetry while avoiding having to re-mirror any feature.
So, I guess this is a solution. However, the problem remains: once 3D Sketches reach a certain level of complexity it isn't possible to mirror them once more. The workaround isn't complicated, but this problem does hamper workflow. Anyhow, if this exploration helps anyone please let me know, or 'like' this reply.