To enable the recording of the watchdog() messages, you just need to enable the Database logging module (short name: dblog). Once you enable it, on admin/reports/dblog you will start reading the recent log entries.

As for the possible error that could return cron, they are the following ones:

• Cron has been running for more than an hour and is most likely stuck
• Cron is already running and you try to re-run it

This is evident from Drupal code. The function that is executed when you go to admin/reports/status/run-cron is system_cron_run(), which returns the error you are seeing when drupal_cron_run() doesn't return TRUE. This is that function code.

  // Try to allocate enough time to run all the hook_cron implementations.
  if (function_exists('set_time_limit')) {
    @set_time_limit(240);
  }

  // Fetch the cron semaphore
  $semaphore = variable_get('cron_semaphore', FALSE);

  if ($semaphore) {
    if (time() - $semaphore > 3600) {
      // Either cron has been running for more than an hour or the semaphore
      // was not reset due to a database error.
      watchdog('cron', 'Cron has been running for more than an hour and is most likely stuck.', array(), WATCHDOG_ERROR);

      // Release cron semaphore
      variable_del('cron_semaphore');
    }
    else {
      // Cron is still running normally.
      watchdog('cron', 'Attempting to re-run cron while it is already running.', array(), WATCHDOG_WARNING);
    }
  }
  else {
    // Register shutdown callback
    register_shutdown_function('drupal_cron_cleanup');

    // Lock cron semaphore
    variable_set('cron_semaphore', time());

    // Iterate through the modules calling their cron handlers (if any):
    module_invoke_all('cron');

    // Record cron time
    variable_set('cron_last', time());
    watchdog('cron', 'Cron run completed.', array(), WATCHDOG_NOTICE);

    // Release cron semaphore
    variable_del('cron_semaphore');

    // Return TRUE so other functions can check if it did run successfully
    return TRUE;
  }

As for why Drupal thinks the cron is still running, that happens when an error in the code (generally one of the hook_cron() implementations) doesn't permit drupal_cron_run() to execute the following line:

    // Release cron semaphore
    variable_del('cron_semaphore');

This means that to debug why cron doesn't work properly, you need to check any hook_cron() implementation, and see what is wrong with them. The problem could also be an implementation of hook_node_view() which is wrongly calling drupal_goto().