In Drupal 7 how do you output array objects to be view able in watchdog error reports?
You can use watchdog but the message part should be translatable, so any variables should use placeholders defined in the variables array. Check out format_string to see how these should work. 

watchdog(
  'my_module_name',
  'Here is the printed variable: &lt;pre&gt;@placeholder_name&lt;/pre&gt;',
  array('@placeholder_name' =&gt; print_r( $my_variable, TRUE)),
  WATCHDOG_INFO
);


Also, convention dictates that the first parameter, $type, should be the module name calling watchdog.