Right, I've looked at this, and the problem is that wesnoth was compiled against boost 1.33.1.
The most recent boost packages in the repos are 1.34.1 (in extra) and 1.35.1 (in testing), and those packages do not contain the library that wesnoth needs.
Slapt-get gets the most recent version of boost as a dependency, because wesnoth says "boost >= 1.33.1".
Ideally the wesnoth package should be recompiled against the most recent boost version in the repos.
For the time being, if you downgrade to boost-1.33.1 it will work.
You never know if this might break something else, though. It's possible that other packages depend on a more recent version, but I don't know for sure.
So, you can also keep 1.34.1 and do:
ln -s /usr/lib/libboost_iostreams.so /usr/lib/libboost_iostreams.so.1.33.1
It's ugly, but the game starts just fine.