Ok, after doing a test at the request of KP9000, I've come up with the following:
The waterfall level with the spinies needs work. The current is too strong, and some of the jumps are rather difficult.
The poison mushroom didn't spawn right away in one of the later levels (you need to hit a P-switch just before it), I'm guessing there was a sprite overflow/cap that was hit.
A couple of times I hit a spinning block and took damage/died. Similar events happened with normal blocks.
Big Bertha's castle: If you hold left while entering the level, you auto-die because you get stuck in the pipe.
I did not beat Big Bertha. Seven attempts landed me one hit on it, at which point I gave up.
I will say that I do like the level design of this, although it took me a while to get used to SMB3's physics again. Look forward to more releases.