Mysql – Incremental/Differential MySQL Backup using thesqldump

Well a packed question, let me try to answer all the issues you raised there.

Binary backups vs dumps

Right now you're using mysqldump to do full backups of your database, that's a good practice indeed but it can get a bit endearing when dealing with huge MySQL installations. Binary backups are good point in time backups, but you need two parts, one full binary backup (which needs to be consistent) and the binary diff logs. Of course the time for recovery for one an the other is drastically different too, it all depends as said on the size of your database and your turnover times.

How flushing the binlogs will affect replication

It won't affect replication if you flush the logs always after they've been transmitted to the slave, otherwise you'll run into some nasty issues due to the slave not being able to request the exact block of the binlog that it needs

At first, try to backup table by table or DB by DB - do not lock everything.

Increase max_connections, try to use connection limit otherwise: http://dev.mysql.com/doc/refman/5.5/en/user-resources.html

I'm not sure it will take too much of memory for increased max_connections.

If you are using MyISAM - there is no other way for backup. With InnoDB or XTraDB - no problems. http://www.innodb.com/doc/hot_backup/manual.html