I feel like I must have a different mobile browsing experience from everyone else, since I think it's a total pain in the backside but I see other people saying they have no problems with it.
I took a screenshot. I closed all my tabs and then opened TLS via a shortcut, and this is what it looked like after it finished loading (I haven't zoomed in or out):
This is with the "mobile narrow" theme. Broken images everywhere, a stretched page, and text that's too tiny to read. I guess it's like Octo said - different browsers produce different results.
Anyway, thanks to Fangu's post, I switched the shoutbox off. I visited that page before making my post and did a ctrl-f search for "shout", but of course it's called a "chatbox" there, so I didn't find anything.