Now I think I know what was broken for me in WP 3.8:
The new, nice admin-interface uses special fonts, which are, fetched from Google when needed. But...
If your main language is, say, English, and then you add a second language which uses a different character subset than English, then this additional subset won't be requested. So for me, all Russian text in the admin interface doesn't have any graphical representation, and is therefore invisible!
In a purely Russian installation, I don't get this issue, since then the WP core makes sure that the correct additional character subset is loaded. Here's what it looks like on one of my sites.
<link rel='stylesheet' id='open-sans-css' href='//fonts.googleapis.com/css?family=Open+Sans%3A300italic%2C400italic%2C600italic%2C300%2C400%2C600&subset=latin%2Clatin-ext%2Ccyrillic%2Ccyrillic-ext&ver=3.8' type='text/css' media='all' />
Perhaps with Qtranslate one needs to somewhere tick a list of what character subsets may be needed for your particular site.
I'll dig a little bit deeper. But, until further notice, I hold back on moving to WP 3.8 for my multilingual sites...