Edit: Yes, I figured it out. In Rails 4.0, the default page for a new app is no longer served as a static file from the public/ directory. Instead, something magical happens, and the magic doesn't work on Heroku. That's no worry, though, as it only means the first app doesn't work. The other apps, which set root routes, should work fine.
They don't, though. I can't get the main sample app's CSS or images to load properly. Hmm... Bleeding edge indeed.
Update: You need to edit the default production.rb file to configure Rails to serve static assets:
config.serve_static_assets = true
Thanks to ninthfrank07 for his link at https://news.ycombinator.com/item?id=5411964 that included the solution.