I stand corrected.
IMO, when this happens, the slur is too close to the notehead. In normal cases, the slur starts/ends two vertical positions above/below the stem/notehead. In NWC's "seek the notehead" scenario, the slurs are a full vertical position closer. My druthers would be to seek the center of the stem, but one vertical position is too close.
Here's a bug and some anomalies:!NoteWorthyComposerClip(2.0,Single)
|TimeSig|Signature:3/2
|Note|Dur:Half,Slur|Pos:-5|Opts:Slur=Upward
|Note|Dur:Whole|Pos:-1|Color:1
|Bar
|Note|Dur:Half,Slur|Pos:2
|Note|Dur:Whole|Pos:-1|Color:1
|Bar
|Note|Dur:Half,Slur|Pos:1
|Note|Dur:Half,Slur|Pos:0
|Note|Dur:Half|Pos:-1|Color:1
|Bar
|Note|Dur:Half,Slur|Pos:4
|Rest|Dur:Whole
|Bar
|Note|Dur:Half,Slur|Pos:-4
|Rest|Dur:Whole
|Bar
|Rest|Dur:Whole,Slur
|Note|Dur:Half|Pos:0
!NoteWorthyComposerClip-End
If you select each of the red notes and toggle Stem Down, the slur changes. It shouldn't. Measure 1 is a bug, the other two are just annoying (and, I suspect related to the discussion above).
In measure 4, select the Rest, and use the +/- keys to cycle duration. The slur bounces around wildy. Contrast this with measure 5, which is much more predictable. In measure 6 the slur even changes direction as the Rest duration is cycled!
Of course, slurs starting or ending on rests are rare.
A suggestion: currently, slurs usually start/end 2 vertical positions above/below the notehead/stem. This means that when they start/end in the staff line area, half the time they start/end on a staff line. This looks less than ideal. If this was changed to 1 2/3 vertical positions, they would never start or end on a staff line, yielding a cleaner appearance.