Just to make sure it is not a problem in the update record server behavior, look for the following code:
$WA_Sql = "UPDATE `" . $WA_table . "` SET " . $updateParamsObj->WA_setValues . " WHERE " . $WhereObj->sqlWhereClause . "";
$MM_editCmd = mysql_query($WA_Sql, $WA_connection) or die(mysql_error());
and change it to:
$WA_Sql = "UPDATE `" . $WA_table . "` SET " . $updateParamsObj->WA_setValues . " WHERE " . $WhereObj->sqlWhereClause . "";
die($WA_Sql);
$MM_editCmd = mysql_query($WA_Sql, $WA_connection) or die(mysql_error());
This will write the UPDATE SQL To the screen try running that SQL statemnt directly on the database using PHPMyAdmin or another tool.
If that works, then check that the username being used in the Dreamweaver Database connection has edit access to the database.