This is a large topic.
There are very large number of permutations to the way documents can be packaged when they are sent to the app.  We attempt to handle them all,  we have undoubtedly missed some.
Some document we cannot legally import due DRM (Digital Rights Management, see the Digital Millennium Copyright Act)
When sharing document from other apps, in newer versions of Android, the sending app must grant the receiving app permission to read the document.  Some apps fail to handle this properly.  Try saving the document, and import the document from the sdcard.
It's a format we could potentially handle, but don't handle yet.
Some web pages cannot be imported via the standard import mechanism.  Examples of pages that won't load: Password protected pages, pages requiring cooking or javascript.   For these cases, use the internal browser, its functionality is rather limited, but it gets around these problems.
We log basic information on import failures (the content type and file extension and the error).  Send an email to support, with your device make and model and when the failure occured, and we should be able to find the log entry for the failure, and then tell you if we can make it work, or if it's one of the issue above that's out of our control.