If you try to upload files on a phone the repository pop-up window (possibly referred to as the "file-picker"? not sure) is too large to use.
I was going to suggest an easy way to test is to try to change your user profile picture on moodle.org, but on visiting to try it myself it never seems to load the file display bit. I just get the spinner gif icon forever.
It's still mostly functional, but the section that lets you switch between different repositories is off the left-hand side of the screen. So if the default is say Wikipedia search, you can type in a search term, and hit the button. You can then select from the images that return. But the bit that's off the left of the screen can't be accessed, even if you zoom out or try to scroll.
Tested on Firefox and default Browser on Android 4.2