There's a good chance a lot of the things I'm going to say have already been brought up and addressed before, but I figured I'd say them anyway:
1. The intro cutscene is too lengthy and long winded, it could easily tell the same story in a much shorter amount of time. The backstory bit is unnecessary exposition for most people who play the game, as they're not going to have probably played SRB1 and doubtfully are going to. The cutscene is slow and feels like it drags with how the text slowly writes itself across the screen, and for first time players it'll give the wrong first impression of the game. Compare to most other classic Sonic games; the first and second games don't even have an inro, while Sonic 3 & Knuckles tells the basics about what you need to know plot-wise in the about ten or fifteen seconds, though it has the downside that it's unskippable. Sonic 3D Blast uses a similar intro as SRB2, but manages to keep it minimal, and it's still much more effective. Plus, with such a long introduction cutscene, it gives the impression that there will be more story throughout the game, but there aren't any other cutscenes at all. It should be much shorter.
2. A small suggestion, as an addition to the previous, to make the story have a bit more impact and feel relevant, Greenflower Zone could have the Grand Eggship flying away in the skybox above you. Would be a nice touch, though I'm not sure how you'd go about it.
3. Most people I show the game to have told me how much they dislike the controls, finding them slippery. I've always thought they could stand to be a bit better, but this isn't really something I've thought much on, so I don't have much to suggest. I just figured I'd throw it on here since I feel I'm not the only one who thinks this.
4. Red Volcano Zone Act 1 in its current state is bland. I figure that this'll be addressed once Arid Canyon Zone is completed, but right now the stage feels so barren to trek across, with only one enemy and a few obstacles to stop you. It's a pretty straightforward shot to the end, with not much variety for subsequent playthroughs. The scenery isn't much to look at either, everything being brown or red. Lava Reef made things interesting by having other colors to contrast with the stage, the blue pipes, the dark green background against the light foreground, but Red Volcano has nothing but rock and lava.
5. Red Volcano Zone Act 2 should also bring back the idea of having snow and ice like Blue Mountain Zone Act 2 was supposed to, but in addition to the lava theme instead of replacing it. It would be a sort of fire and ice stage, the upper paths having ice and snow and an open cloudy sky, but having ways you can easily fall back down to the lava sections underground below. Gimmicks could include ice and rocks crumbling to close paths below and open ones above it, but if you're quick enough you can get through to get to more difficult but more rewarding paths.
6. I figured I'd add my two cents on the whole Dark City/Grand Eggship debacle, as those were the stages I always looked forward to even back in the 1.09.x days. Perhaps the two stages could be merged, in the same way Mine Maze and Rocky Mountain became Arid Canyon. The first act could be just the city with the ship in distance, the second act could be the ship itself or boarding the ship, and the third act could be the Brak Eggman boss, with the final boss being something new entirely. As to how the level would play, since it's the penultimate level, it should be similar to Starlight and Stardust Speedway in that it's the games fast paced yet dangerous zone, in the same way Egg Rock puts your platforming skills to the test like Scrap Brain and Metallic Madness do. Perhaps look to those levels for gimmicks.
7. This is probably just me, but Egg Rock as it stands is way too hard. No matter what path I take I always end up dying, and I've never gotten past Act 1. It's not even just that I think it's too hard for the game, it's that the difficult curve is so sudden and unfair in comparison to the easy to breeze through Red Volcano Zone. I guess I don't play the game nearly as often, so for a lot of people here it's probably easy, but it really could be toned down a notch here and there. Particularly the crusher section where I have no idea what I'm supposed to do to get through, if that's still in. I haven't gotten that far since 2.0.