I think the biggest factor is straight arrows, after you have those you need to make sure the ends are cut true, I don't always see a big difference in squaring the ends of my shafts, however my saw is setup just right, a poorly setup arrow saw can really mess up the cuts. I used to spine align the arrows on a spine tester, found that to be a waste of time but nock tuning before fletching has shown to be worth the time, that might even be better than the straightness actually.
For starters you need arrows that spin evenly, broadheads that don't wobble, nocks that make even contact on the shaft. I have some arrows that just flat out won't shoot, can't figure it out, they seem fine in every way I can check them. I have seen a nock make an arrow fly 4" low at 20 yards, no outward evidence why, just could put that nock on a different arrow and it would do it to that arrow as well.
Those are factors that pop out at me immediately, I'm sure I'll think of more as time allows.