I've found a solution here:
http://forums.mysql.com/read.php?113,57867,176468#msg-176468
so you have to download a package from http://www.wesmo.com/rpm2html/contributed/RPMS/MySQL-shared-compat-4.1.9...
and change
VendorLibLinux=libmysqlclient.so to VendorLibLinux=libmysqlclient.so.10
at ~/DBDesigner4/DBConn.ini and ~/DBDesigner4/DBConn_DefaultSettings.ini

For installing MySQL-shared-compat-4.1.9-0.i386.rpm package in debian:
$ sudo alien --to-tgz MySQL-shared-compat-4.1.9-0.i386.rpm
$ sudo tar xzvfp MySQL-shared-compat-4.1.9.tgz -C /

Blessings!