I've seen that too, actually, Unity not rendering all the text. And yes, as far as I could tell too, it still worked, even allowed editing, it just didn't render all of it. I'd guess it's not really built for text-heavy applications. (At least not without some end-programmer effort to do things like split the text up into more manageable chunks.)
I don't see it much, though, probably in part since I've taken to minifying my code before pasting it in - not so much because of this, but because it means I don't have to scroll so much after pasting it in. (It's pretty easy to do, even - I just have the preprocessor output open in my editor, and use its regex replace to remove all instances of \s*//.*$ before I copy what remains. I've been thinking of making the preprocessor do it, but haven't bothered yet - dunno if I will.)
In theory, one could pull off essentially anything (computation-wise anyway) with it. In practice, though - what someone actually manages to do - yeah, that's where the interest lies, indeed. :) (I'll probably not do much/anything with BF myself, as making the asm do what I want in the space I have is tricky enough, but I certainly don't mind if others do.)
I'll note that clockspeed isn't the only problem for this with the default mode, I'd think the disk space is a bigger problem. I haven't tried it, so I'm making assumptions here, but I figure that anything even semi-significant having been compiled down to BF is likely to be large - and there's not really much space available here.
Also, the output method this interpreter uses means that it's even more limited than usual in user interaction, so game-type stuff is rather limited by that. OS-type stuff similarly. The thing about Turing-completeness is that it only talks about computation - and a lot of what modern computers do isn't really about that, instead involving things like real-time user interaction. Sure, a program on a Turing-complete computer could simulate such user interaction - but then it wouldn't be actual user interaction, now would it?
Still, even with those limitations, there's quite a lot that is possible. All it needs is for someone crazy enough to actually do it to come along... :)