I also was especially impressed by the hyperspace effect in the Falcon, the new Death Star introduction, and especially the improvements to the battle of Yavin. Many people have expressed dislike for it, but I heavily disagree. It now feels more like a real battle, and not so small scale. Plus, when red group reports in you can hear pilots like red 7, red 9, or red 11. We never saw how they die, but this new edit helps explain it. Great work, and must have been very difficult I can imagine.
I'm also impressed with the sound. I don't know how you did it, but many of the characters voices sounds much less 70s and muffled. It really makes a the film a lot less dated. Well done! I'm unsure about Beru's voice though. It does sound more natural, like it's actually her speaking, but I can se why Lucas dubbed her: she just isn't that good an actress. I think she rushes through her lines with too little emotion inflicted. But everyone will feel different on this one, and I really am fine with the new voice since it has the plus of sounding more genuine.
Of course I don't agree with everything. The imperial march, if put into ANH, should be a bit more low-key and subtle instead of the fullblown ESB theme. And the scene in Ben's hut really didn't need to be altered (although it was pretty cool to get an alternate take). But these are minor concerns. You have really showed Lucas and his minions how it should be done. And you did by yourself. There are still things that I would like done, like change Vader's IMO oudated voice and score a new music for the Obi-Wan-Vader duel, but that is completely out of your control. It would require Jones to re-score his lines and for Williams to write a new piece.
Finally, I just want to say congratulations. You've made the best version of ANH there ever was.