There are times when I want to listen to a lengthy audio file but playing it in the Dropbox  player or Droplr player just doesn't work as well as something purpose-built for long-form files. In those native players, there are no bookmarks and until recently I wasn't aware of ways you could cache them on your device so if I was in an area of spotty connectivity, it was next-to-impossible to listen to what I wanted.
In trying to solve this problem, I found a little-touted feature in Downcast which allows you to add an audio file in amongst your podcast feeds via a URL. The file will act like a podcast for all intents and purposes allowing you to play it at faster-than-normal speed, bookmark it when you exit the app, skip forward and back, etc. I've been trying to work my way through dozens of hours of lectures and talks and this feature has been invaluable.
The problem I was facing was that Downcast needed a link to a physical file -- not a link via Droplr or Dropbox which use link re-direction. Trying one of those links in Downcast results in a file error and frustration. After several days of trying different services or techniques, I wrote to the Downcast team and asked for help. It turns out that it was entirely possible to make this work with Dropbox. 
Here's what you do to import a file from Dropbox into Downcast:
- Open the native iOS Dropbox app.
- Navigate to the file and open it.
- Tap the star to "favorite" the file. This also downloads it to your iOS device cache.
- Click the little "outbox" folder on the bottom right and select "Open in Downcast".
- This will import the cached file into Downcast.
- Go back to Dropbox and un-star the file to delete the cache -- no need to keep two copies cached.