Mega Man 3 improves over the second game in many ways: particularly, it's faster. Climbing, screen transitions, and health pickups occur more hastily. There is now a slide maneuver that makes your character faster.
The game has some of my favorite music, bosses, and stages of the entire series. Particularly, the Wily 1 boss is now at a reasonable difficulty rather than being more difficult than any of the bosses that follow it (unlike the first two games).
Protoman is introduced here, but I don't really like him. He just becomes a boring obstacle and doesn't add much to gameplay. I suspect he was supposed to make the player curious about who he was. I think the game would be an improvement without all excessive fights against him. Not sure why he puts on a mask and calls himself Break Man.
Mega Man's dog Rush also first appears in this game, and it was a clever way to unify the platforming weapons you got from the robot masters.
One thing I noticed during this playthrough is how very hard enemies hit you, and how easy it is to get swarmed. I felt myself getting harassed and getting my ass kicked constantly. The Energy Tank capacity is raised to 9, but I would have preferred they left it at 4 and made enemies deal less damage.
I need to start by addressing how messy Mega Man 3 is as a game. There are a lot of objects used haphazardly and this results in a sometimes flickery/glitchy screen thanks to how 3DNes negotiates these objects. In particular, text is required to be in the foreground and background at so many different points that you're left with a very jagged mess, even at the title screen.
Opening the menu is a real disaster, since it doesn't wipe the screen first. As a result, the menu tends to take properties from objects that are on screen at the time. I did not finish the menu fully, because I couldn't reasonably do so. There are far too many places where it will glitch out. If you change the menu at any point, be prepared to see something elsewhere in the game fall out of sync. It's better to learn to live with it.
While I wrapped up my work on this game and did a playthrough of it on my Twitch channel, geod showed up and gave me some great advice on how to use the Delete feature. In Hard Man's stage, many many objects were loading and re-loading as new objects thanks to ladders and surfaces melding with surrounding objects. When this happens, there may be a separate object for e.g. the ladder, and one for the ladder with a bit of ground attached to it. This is going to run up your filesize and drive you crazy. If a ladder (or anything) starts to glitch out after you've already set it, delete the new glitched sprite of it. It may revert back to the correct version.
From here it would just be better to talk about each stage that has peculiarities.
Magnet Man: Early in the stage, you'll see the ceiling "glitching" out, as the ceiling can't decide how to define itself as an object. You may have luck with the Delete button, but it doesn't hurt much to leave it alone.
Gemini Man: As of v1.1b3, there is a graphical glitch during the "outside" portion of the stage where the surface of the ground doesn't render properly, and follows you through the stage.
Hard Man: I had to go with "Char" rendering on nearly every rock surface because of how glitchy the level was, since it re-generated terrain constantly.
Top Man: Unfortunately, like with Crash Man in MM2, most of this stage is on the same layer and looks flat. This is because the background is an object and portions of it are shared with other levels.
Spark Man: I love how this stage turned out. Everthing rendered pretty much the way I wanted, and I had some fun with the background Van de Graaff generators, especially during the Doc Robot revisit.
Shadow Man: The whole "plunged into darkness" concept is ruined because of how objects still render light diffusion and shadows. Think "Quick Man" in MM2.
The Wily stages generally look good, and there are plenty of recycled ground assets, which made my life easier. The "Cube" rendering glitch that causes surfaces to look like shelves happens here sometimes, but that's about it for the whole game.
Wily 3 has a couple screens with moving platforms. The Gemini Man ground glitch appears here too, which makes for some increased difficulty in the platforming, since you need to get used to ignoring the parts of the ground that are illusions. Or you could take Rush Jet through.
This game was a bit stressful and I have to get busier with my academic work. I don't know how long until I get into Mega Man 4.