Reset the password to pre-4.1 style for each user that needs to use a pre-4.1 client program. This can be done using the SET PASSWORD statement and the OLD_PASSWORD() function:
mysql> SET PASSWORD FOR
-> 'some_user'@'some_host' = OLD_PASSWORD('newpwd');
Alternatively, use UPDATE and FLUSH PRIVILEGES:
mysql> UPDATE mysql.user SET Password = OLD_PASSWORD('newpwd')
-> WHERE Host = 'some_host' AND User = 'some_user';
mysql> FLUSH PRIVILEGES;
