My guess would be that for some reason mysql.so did't get linked at all against libmysqlclient.so (at build time of the module).  Alternatively, if it was linked, it might be pulling in a wrong version of the library at runtime, which doesn't provide the symbol mysql_init — that's unlikely, though.

What does ldd /usr/local/lib/perl5/auto/DBD/mysql/mysql.so  say?