The link Namdia gave me had the answer!

So, if you go into your settings in DOSBox, switch the "machine" setting to vgaonly and that will resolve the issue.

As for the music, I would chalk it up to the limitations of the system. Probably, on the hardware it was programmed for, it works great, and I'm trying to play it with later end DOS emulation. Or maybe I had a bad sound card growing up. Maybe I always selected the wrong option.

Thanks for the assist!

I'm aware of Lemmix and NeoLemmix, though I didn't know the goals behind them. My question was more to do with like... how widespread are these problems? Is this something everyone deals with? Am I remembering correctly that the graphical error was there in 1994, or is that a fabricated memory?

I just don't know, and it's kinda driving me a little mad.

As for the music, yeah, I'm pretty sure the off-notes were there in the old version, but I'm pretty sure there was a way to make it sound right too. But maybe that's just wishful thinking. Like, what's the best version of the original game you can get? The... Most True to the Original Vision of the game, I guess. I feel like the SNES and Genesis versions are lacking dramatically due to the lack of Mouse support, and I'm not all that fond of the requirement that every screen have music on it. I kinda liked the silence before and after each level.

I've got the game running on DOSBox, and for the most part it works great. I feel like I'm 7 again. But... there's a couple problems.

First of all, all the start screens for the stages are incredibly difficult to read due to a color error. Now, I think I've had this problem every time I tried to play the DOS version, including all those 25 (or more) years ago, so it might just be a design flaw, but I've noticed when I see Let's Players doing videos online, they don't have that problem. It looks normal, like the end of level screens.

Here's a screenshot:
https://imgur.com/Gp6cGGU

As for the music, well, again, this is probably more due to the DOS version just being funky, but a lot of the notes are in the wrong place. I've heard DOS versions that sound better, but I'm not sure how to make that happen. Is there a way to emulate a better sound card? Alternatively, maybe I should just try to get an Amiga emulator working?