Ultimately I caved in and looked up on the internet what I had to do to progress in Zelda: Minish Cap. When I found out what I'd missed I was really sad at myself. It turns out there are 4 ways out of the main town: 1 that you can come in through and 3 that are guarded by guards. Apparently if you talk to one of the guards in particular he'll let you out. I'm not sure if I talked to him earlier and he wouldn't let me out (you need to learn spin slash) or if I'd talked to the first two and assumed the third guy was the same.
Very shortly thereafter I got stuck again. I was exploring a mountain and couldn't find another way to go. It turns out you need to use your vacuum cleaner thing on globs of white goo to reveal a cave. I'd swear I'd used every item in my inventory on the white goo. It wasn't that I didn't think to use the vacuum cleaner... It's that I thought I already had! This is likely an issue with playing the game in 10 minute chunks on the bus/subway. Sigh.
I just had to look something up for the third time. In this case I was pretty sure I'd explored all of a dungeon. There were big sand dunes all over the dungeon and I could see treasure behind some of them. I couldn't find a way to get through. This time I double checked all my items to no avail. It turns out you need a special item to dig through the sand dunes. That item was found in the dungeon. Behind a wall you could explode with a bomb. An unmarked wall...
This reminds me a little bit of Final Fantasy Adventure. That game was filled with unmarked walls you had to knock down in order to progress. I ended up playing that game with a map open on my computer as I got so fed up with trying to knock down unmarked walls. I hate the concept. Now, if it was a sidequest or something I'd be ok with it. Want to hide a quarter-heart of a gold skulltula behind an unmarked wall? Fine. Annoying maybe, but fine. Forcing me to explode every wall on the off-chance it's the way I need to go in order to make progress? Terrible.