Another post thanks to Many Tricks' Peter Maurer; this particular bug bit me last night—I spent 30 minutes trying to figure out why a compiled AppleScript with a droplet wasn't working. I never did get it, so I emailed Peter, and he pointed me to these tweets from a while back…
…which means the app won't launch. You have to "chmod +x applet" manually to make it work.
— Peter Maurer (@petermaurer) March 14, 2017
And yea, that was the problem: As soon as I added the +x to the compiled script, everything worked as expected. The exact syntax is:
chmod +x /path/to/compiled.app/Contents/MacOs/droplet
I'm documenting this here so that I can find it more easily the next time I save a compiled droplet AppleScript and forget about this not-so-little bug.