Well, I tried v3.47 final, and it did much better in terms of downloading the
whole site properly.  For one thing, the files it created on disk kept the
original Russian (Cyrillic) names where applicable.  V3.48 had not done that.

But when I tried to browse the mirrored site I found the same problem -
nonsense chars in the links which just brought up error screens.  However,
that was with Internet Explorer 10.  When I thought to try Chrome, the
mirrored site works fine!  The failure with IE is surprising because it will
browse the original Wordpress site fine; it just can't browse the mirrored
site.

So I still think there are issues with v3.48 because it doesn't appear to
download the site properly.  But the user needs to be aware that the browser
matters too.  I have to admit that I don't know where any fault lies at this
point.