The concern with adding your dry hops during active fermentation is that you will lose that precious hop aroma out of your airlock as the CO2 is still escaping. I know some breweries (21st amendment IIRC) do add some of their dry hops towards the very end of active fermentation, however, they cap their airlock so nothing escapes (I assume stainless steel fermenters can contain the pressure buildup much better than a carboy or bucket). The advantage is that as the hop pellets disintegrate and fall to the bottom the rising CO2 bubbles lift them back up and keep them in suspension, which means you get more hop bang for your buck (and who doesn't want that!).
I used to dry hop in the fine mesh nylon bags in my primary, but I have since started dumping the pellets straight into the primary a week before kegging. I have found that cold crashing, even just for 24 hours, makes a huge difference on how quickly and fully the hoppy bits settle out, however I have also been zip tying a fine mesh nylon bag to the end of my racking cane, which helps a lot too.
Oh, and I regularly leave my beers in the primary for 3-4 weeks before kegging, with no off flavors at all. The concern with autolysis comes mostly from the large commercial cylindrical conical fermenters, and has more to do with the weight and pressure of the beer put upon the yeast in the bottom of the fermenter cone. Using broad bottomed buckets or glass carboys for homebrewing doesn't seem to create that problem.
