How to log verbose output from mysqldump?

Your 1st mysqldump makes table structures and INSERTs and puts it in dump.sql.

Your 2nd dump is a remote dump that is piped straight into mysql in localhost.

If you are trying to catch any output based on errors, try this:

mysqldump -alv -h 123.123.123.123 --user=username --password=p@ssw0rd --add-drop-table databasename 2> output.log | mysql --user=username --password=p@ssw0rd -h localhost localdatabase

Using 2> will catch any error-based output (aka stderr). The mysqldump should still pipe normal console output (aka stdout) to the other mysql session and load the data as intended.

EXAMPLE : I have a small database called sample on my PC.

I ran this:

C:\LWDBA>mysqldump -u... -p... --verbose sample 2>sample.txt > sample.sql

C:\LWDBA>type sample.txt
-- Connecting to localhost...
-- Retrieving table structure for table users...
-- Sending SELECT query...
-- Retrieving rows...
-- Disconnecting from localhost...

C:\LWDBA>type sample.sql
-- MySQL dump 10.13  Distrib 5.5.12, for Win64 (x86)
--
-- Host: localhost    Database: sample
-- ------------------------------------------------------
-- Server version       5.5.12-log

/*!40101 SET @OLD_CHARACTER_SET_CLIENT=@@CHARACTER_SET_CLIENT */;
/*!40101 SET @OLD_CHARACTER_SET_RESULTS=@@CHARACTER_SET_RESULTS */;
/*!40101 SET @OLD_COLLATION_CONNECTION=@@COLLATION_CONNECTION */;
/*!40101 SET NAMES utf8 */;
/*!40103 SET @OLD_TIME_ZONE=@@TIME_ZONE */;
/*!40103 SET TIME_ZONE='+00:00' */;
/*!40014 SET @OLD_UNIQUE_CHECKS=@@UNIQUE_CHECKS, UNIQUE_CHECKS=0 */;
/*!40014 SET @OLD_FOREIGN_KEY_CHECKS=@@FOREIGN_KEY_CHECKS, FOREIGN_KEY_CHECKS=0 */;
/*!40101 SET @OLD_SQL_MODE=@@SQL_MODE, SQL_MODE='NO_AUTO_VALUE_ON_ZERO' */;
/*!40111 SET @OLD_SQL_NOTES=@@SQL_NOTES, SQL_NOTES=0 */;

--
-- Table structure for table `users`
--

DROP TABLE IF EXISTS `users`;
/*!40101 SET @saved_cs_client     = @@character_set_client */;
/*!40101 SET character_set_client = utf8 */;
CREATE TABLE `users` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `users_tbl_points` int(11) NOT NULL,
  `users_tbl_rank` int(11) NOT NULL DEFAULT '0',
  PRIMARY KEY (`id`),
  KEY `users_tbl_points` (`users_tbl_points`)
) ENGINE=InnoDB AUTO_INCREMENT=31 DEFAULT CHARSET=latin1;
/*!40101 SET character_set_client = @saved_cs_client */;

--
-- Dumping data for table `users`
--

LOCK TABLES `users` WRITE;
/*!40000 ALTER TABLE `users` DISABLE KEYS */;
INSERT INTO `users` VALUES (1,785523,9),(2,443080,20),(3,858830,7),(4,964909,3),(5,248056,24),
(6,345553,21),(7,983596,2),(8,881325,6),(9,455836,19),(10,635204,16),(11,808514,8),
(12,136960,28),(13,259255,22),(14,885399,5),(15,649229,15),(16,589948,18),(17,2055,30),
(18,240429,25),(19,195981,26),(20,258620,23),(21,705158,12),(22,749931,11),(23,634182,17),
(24,921117,4),(25,703038,13),(26,751842,10),(27,650093,14),(28,994943,1),(29,24437,29),
(30,137355,27);
/*!40000 ALTER TABLE `users` ENABLE KEYS */;
UNLOCK TABLES;
/*!40103 SET TIME_ZONE=@OLD_TIME_ZONE */;

/*!40101 SET SQL_MODE=@OLD_SQL_MODE */;
/*!40014 SET FOREIGN_KEY_CHECKS=@OLD_FOREIGN_KEY_CHECKS */;
/*!40014 SET UNIQUE_CHECKS=@OLD_UNIQUE_CHECKS */;
/*!40101 SET CHARACTER_SET_CLIENT=@OLD_CHARACTER_SET_CLIENT */;
/*!40101 SET CHARACTER_SET_RESULTS=@OLD_CHARACTER_SET_RESULTS */;
/*!40101 SET COLLATION_CONNECTION=@OLD_COLLATION_CONNECTION */;
/*!40111 SET SQL_NOTES=@OLD_SQL_NOTES */;

-- Dump completed on 2012-03-02 15:49:54

C:\LWDBA>

Give it a Try !!!

mysqldump -v outputs to the stderr stream so you just need to redirect that

mysqldump -alv -h 123.123.123.123 --user=username --password=p@ssw0rd --add-drop-table databasename 2> dump.log | mysql --user=username --password=p@ssw0rd -h localhost localdatabase

example

 foo@bar: ~ > mysqldump -v -u root mysql > /dev/null 2> output.log
 foo@bar: ~ > cat output.log 
 -- Connecting to localhost...
 -- Retrieving table structure for table columns_priv...
 -- Sending SELECT query...
 -- Retrieving rows...
 -- Retrieving table structure for table db...