Will a loose nock cause erratic arrow flight?  I have a Death wish longbow that had perfect arrow flight.  The arrow rest was wearing out so I replaced it. Same size and thickness. Nothing else changed. Now I can't get good arrow flight. I tried thicker and thinner arrow plates. Tried to retune the bow, raised and lowered the brace height and nock, one adjustment at a time. Still arrows wagging left/right, mainly tail kicking left. I'm running out of ideas, so I thought it might be loose nocks. Any help will be appreciated.

To answer your question, yes loose nocks (i.e how tight they fit on the string) can cause problems sliding down the string at release if you don't have a second nock-set under them.  Dry fires are the bigger concern if they detach completely during your draw.  Changing your rest material did not alter your nock fit, though.  What rest material did you use?  You state that it was the same thickness....as the worn out material or the material when it was new?(assuming it was shooting fine with the worn out material until it was removed.placed)

I make arrows with self nocks and I've always made loose. I prefer them loose and I nock my arrows over the nock point. Just the way I've always done it. I don't hang my bow when hunting. It lays across my lap when sitting or held in my hand when standing.