...And this is the point when I realized that I was, in fact, not in the clear for World 1.
I noticed that I had collected a coin when beginning 2-1, and was confused. But when I finished the level, I saw the coin counter go up again. I realized this was due to a Pile Driver Micro-Goomba being on screen when I ended the level. It was automatically killed and became a coin that I picked up. A similar instance occured in 1-5 with a Paratroopa, though I didn't notice at the time. So that's a load of crap. Now I have to lead all enemies away from the Goal square before ending a level. Hopefully this doesn't become too much of a problem later on, but I'll have to see. Luckily, 1-5 and 2-1 are still perfectly beatable, but I'll need to keep an eye out.
World 2
Level 2-1 Oh what fun. Pile Driver Micro-Goombas. These are infuriating to deal with, but the level's possible. Make sure to get rid of one near the Goal square, or it will turn into a coin you automatically collect.
Level 2-2 I took the underwater route for this level, since there's a lower chance of running into any enemies or coins.
2-Midcastle No coins, but this was my first encounter with a Boo, and god they move fast in this game.
Level 2-3 *screams of agony commence* This level is really tricky to get through. There's a segment at the end where you have to break some blocks with a Koopa Shell to uncover a pipe leading to the exit. Unfortunately, some of these blocks contain coins. To avoid hitting these blocks, I had to enter the level with a fire flower, kill the koopas, then return with a Tanooki Leaf and break the blocks myself, avoiding the ones with coins. Overall, very frustrating.
2-Quicksand No respite here! The Angry Sun plauges this stretch of sand, and while it's rather easy to avoid, it turns into a coin at the end of level. Luckily, I can use a Koopa Shell to kill it, avoiding any unnecessary monetary gain.
Level 2-4 I opted to skip this one and take the path through 2-5 instead. It seems possible, but there are some tricky jumps I don't feel like getting around for now.
Level 2-5 This level is fairly easy until the end, where a Chain Chomp lies. I once again need the help of a Koopa Shell to dispatch of it without earning any coins.
2-Pyramid Not too much difficulty here, though I made sure to use my Tanooki Tail to break the blocks, in order to stay on the safe side. The Boomerang Bro near the end shouldn't get close enough to be coin-ified.
2-Airship Once again, not too many coins. Morton's a bit more eager to use his wand, so watch out! The princess gave me a cloud, which is likely to save the run later on.