I've only seen these in Chrome on Android. No idea if they're reproducible. First, potentially relevant device specs:
Device: Samsung Galaxy S6
OS: Android 6.0.1 (all bugs also seen on prior versions)
Chrome Version: 50.0.22661.89 (and various prior versions)
Most Visuals Missing
Intermittently, all visuals except for the UI overlay fail to render. This usually happens if Chrome has been inactive for short time, but not long enough to trigger the force-refresh. I haven't found a reliable process to trigger this behavior.
This appears to be a visual bug only. It is still possible, though no map or unit elements are displayed, to select them and move them around if you know where they are. The UI overlays still appear if you happen to touch a unit, for instance.
Refreshing the page (not just the game data) fixes this bug. There is also one other, more interesting way to fix it, which only works if the browser navigation bar is hidden. When this bug happens while the navbar is hidden, pulling down near the edge of the screen (to unhide the browser navbar) suddenly causes everything to render again.
In the Unit Details overlay, selecting a follower almost always takes several tries. The button registers that it has been pressed (it gets its
:active coloring), but otherwise nothing actually happens. I haven't found any obvious correlations with tap length or anything else; eventually it just decides to work.
Those are the two I encounter the most often; I feel like there's another one that I'm forgetting so when I remember it I'll let you know.