Re: bullet alignment issues?
Likely a bit out of round chamber; if the problem is at the back near the web of the case it may take a couple of firings for the brass to fill there.
FL sizing will likely let you shoot anyway as it'll get the brass sized down so the out of round spot on the case isn't wandering in the chamber as it is when you just neck size.
Another fix is to index your brass with a marker or file; you'll get them in the chamber at the same alignment every time then. Much to anal-retentive for me though; I'd just fl size and forget it.