I just noticed this question, and should probably chime in -- as mentioned above, my company's product, Querki, has its UI now built entirely in Scala.js. That's about 8k SLOC of Scala, last I checked: not the biggest program in the world, but a lot more complex than most sites. I would guess that it's replacing what would have been 20-30k SLOC of JavaScript, and is really the only way the company is plausible at all.
That's beta for a small company, but very much in production, and it's been a godsend: the SJS code is vastly easier to write and maintain than the JavaScript it replaced, and much more stable in practice. Also, hooking the SJS front end up to my Akka/Play back end speeds up development enormously, and reduces bugs, since the API is strongly-typed and boilerplate-free, in end-to-end Scala.
Since folks have asked: the optimized JS code is currently about 1 Meg, and growing quite slowly now that all my infrastructure is written. (Plus about as much again for the JS libraries I use.) That's not trivial, but it's a one-time load per release; once it's cached in the browser, the UI is extremely fast, much quicker than the dynamic pages that had been there.
Oh, and since you're looking for a fully-worked example: the source code can be found on GitHub. That's open-but-restricted, since it's a commercial product, but feel free to dig around and use it for inspiration. (And feel free to request useful bits out of it: I'm gradually lifting broadly-useful bits and pieces into MIT-licensed libraries.)
