When I stop a scene or click on the next scene midi notes stick and continue to sound.  Muting the tracks in the track pane is the only way to stop them.  Is there some setting I am missing?  Or is it a best practice to only have audio clips in The Matrix matrix?

Just had a similar problem. In my case, a loop point set in the piano roll was just short of the exact beat, and dragging the loop point to the beat fixed it. I guess the midi clip was looping before the note off and so any note that was sounding when clicking on the next column wouldn't get turned off, and yes, I think audio clips are much less trouble.