mysql-binlog-dump: command not found

Maybe Your $PATH variable doesn't contain the default paths? echo $PATH should give something like:

[root@server ~]# echo $PATH
/usr/local/sbin:/usr/local/bin:/sbin:/bin:/usr/sbin:/usr/bin:/root/bin

If it's empty, You may set the PATH variable with this command

export PATH="/usr/local/sbin:/usr/local/bin:/sbin:/bin:/usr/sbin:/usr/bin:/root/bin"

On CentOS possible default full paths are:

/usr/bin/mysql-binlog-dump - from package: mysql-proxy

You may install the required package with command yum install {package}

On Debian possible default full paths are:

/usr/bin/mysql-binlog-dump - from package: mysql-proxy

You may install the required package with command apt-get install {package}

Error in other languages:
mysql-binlog-dump: bevel nie gevind nie
mysql-binlog-dump: comandă negăsită
mysql-binlog-dump: comando não encontrado
mysql-binlog-dump: commande introuvable
mysql-binlog-dump: command not found
mysql-binlog-dump: käsku ei ole
mysql-binlog-dump: không tìm thấy lệnh
mysql-binlog-dump: komanda nerasta
mysql-binlog-dump: Kommando nicht gefunden.
mysql-binlog-dump: kommandot finns inte
mysql-binlog-dump: komut yok
mysql-binlog-dump: nie znaleziono polecenia
mysql-binlog-dump: níor aimsíodh an t-ordú
mysql-binlog-dump: no se encontró la orden
mysql-binlog-dump: no s'ha trobat l'ordre
mysql-binlog-dump: opdracht niet gevonden
mysql-binlog-dump: parancs nem található
mysql-binlog-dump: perintah tidak ditemukan
mysql-binlog-dump: príkaz nenájdený
mysql-binlog-dump: příkaz nenalezen
mysql-binlog-dump: команда не найдена
mysql-binlog-dump: командата не е открита
mysql-binlog-dump: 命令找不到
mysql-binlog-dump: コマンドが見つかりません