When I drag a note in Piano Roll View to a different note position, Sonar X1 leaves behind a duplicate note with a very short duration. Then I have to erase that leftover note each time. Very annoying (and obstructive if I don't catch that leftover note). Is there a setting that will eliminate that or is it a bug?

Right offhand, I can't think of an issue or procedure in SONAR that would create a "duplicate" of a different duration in that scenario. It seems more likely the short event it was already there, and moving the longer note revealed it. Or possibly you're looking at events on multiple tracks that share the same pitch...?
 
Have you checked the Event View before dragging to be sure that  short note wasn't already there, hidden by the longer one? Maye on a different channel? Is this MIDI you recorded in real time from a controller or sequenced in the PRV or downloaded from somewhere or...?
 
 

If you are in edit mode and you just click the mouse anywhere, it will create a note. Are you sure that you get the cross-arrows before clicking?
 

using the smart tool ?

...or pressing Ctrl-key while dragging would leave the original note intact.

There are ways that those short ghost notes can appear on a track, especially in pre-X3d versions. See here.
 
By any chance, does the OP have any VSTis sending MIDI events out?