I've shot drop-away rests since they first surfaced on the hunting market around 1996 or so. Barner was making them for target shooters long before that. Based on my own experiences and what I have learned from experts, here is what I have been able to conclude about arrow flight with drop-away rests.
Arrows Need Contact for Stability
Experts who use high-speed cameras tell me a drop-away rest should ideally contact the arrow for six or seven inches of its forward travel in order to stabilize the arrow against the incredible acceleration it undergoes as the string whips forward. You will accomplish this most easily by following the manufacturer's directions when setting up the rest. I have found that if the rest hits full height with the string about an inch short of full draw, the rest will stay upright and help to stabilize the arrow for several inches of the arrow's forward travel. This is because the rest arm has inertia and it takes a split second for the rest to start moving out of the way when the string is released.
Nock Travel is a Big Deal
If you are shooting a bow that doesn't have perfect nock travel, you will not be able to tune the bow with a drop-away rest. This is probably the main reason some bows don't tune with drop-away rests.
Perfect nock travel means the nock moves level (up and down) and on-line (not wavering to the side) as it streaks forward. If it deviates from the perfect route, it pushes the nock of the arrow to the side. With a drop-away rest, there is nothing to nudge the arrow back on track. The arrow is free floating and can take on the movement of the string, causing it to slash noticeably. So first off, your bow has to exhibit excellent nock travel for a drop-away rest to produce good arrow flight.
How You Pull Through the Release
If you pull the release to the side at full draw, you can produce poor arrow flight. This most often occurs when the draw length is too long or too short or if you simply have the habit of pulling it to the side. This will produce the same kind of poor nock travel (though not as severe) as you would see with a poorly built bow.
My mistake was pulling the string across behind my shoulders at full draw. Once I figured this out - it took a few years - and started focusing on making sure I was pulling the release straight away from the target, my arrow flight problems went away. I also shot better. So that is another thing to keep in mind when trying to tune a drop-away rest.
There may be other issues that can affect arrow flight with a drop-away rest too - such as a chord that is too tight - but if you follow the manufacturer's directions for installing the rest, most of those problems should be eliminated. The real problem is poor nock travel - whether inherent to the bow or created by your release technique.
If you just can't get your arrow flight smoothed out short of buying a new bow, it would be much cheaper to buy a rest such as the Whisker Biscuit (or one of the similar models that have hit the market in recent years) to see if more contact with the arrow will keep it on track.