This is one of those glitches that is hard to pin down, but I’d like to report it anyway. On my mobile phone browser (Chrome, Android 6) it sometimes happens that the slide-up screen (coming up when you tap the progress bar) gets stuck, making the page unusable until I reload the page. I think it might happen mostly while composing, but I’m not sure. By “stuck” I mean that it won’t go away when I tap an empty area of the screen.
Another issue that I just had at the same time (though it may be unrelated) was that the message I had composed had disappeared after I navigated to an external page. I had been under the impression that discourse would still remember the autosave message, but in this case it was simply gone (already before I had to reload the page due to the slide-up thing and it did not come back after the reload either). The good news is that when I opened the same forum on my desktop computer, and did the same “reply as new topic” as I had originally done, my saved message magically reappeared! I think I did the same "reply as new topic"on my phone too, without the message reappearing, but I am not 100% sure that I did.
So while the saving of unfinished posts across devices and despite leaving the forum website is a killer feature, the mobile UX can still be improved.
And while I’m at it: I think the UX for new users could be improved by putting some kind of “close” icon or slide down icon onto that slide-up thing because it is easy to trigger it accidentally so that the user is confused and then gets even more confused when s/he doesn’t see a button to get rid of it again ( I would put it next to the notification settings button at the bottom).