Text Editor on iOS that can edit files from any folder in Dropbox
There's a large number of applications available that can do this.

My preferred text editor happens to be Byword. By default, it'll link to a specific dropbox folder (/Apps/Byword), but you can change this in the app's settings; just setting it to "/" will give access to every folder in your Dropbox.

iA Writer is another popular choice.

If you're looking for something more geared towards code than writing, Textastic is nice.

Additionally, Brett Terpstra has compiled a large list of iOS text editors and features here, though it doesn't specify which apps have full access or if they are limited to a specific App folder in Dropbox.