There are a couple of documents that I have on dropbox, that can be opened without an Internet connection of any kind, meaning no 3G and no Wi-Fi. There are other documents that I have on dropbox that cannot be opened unless I have some sort of network connection. Why is this?
If on your iPhone or iPad, there's a local copy stored in the app on your device and the app is putting a copy on Dropbox. The other documents aren't also stored locally on the device, so they need to be fetched before opening.
Dropbox help says to hit the star button if I want to keep a copy of the file for off-line use. The file that I can see without any Internet connection does not have the star button pressed, so I don't know what's going on.