How to add custom operation to commerce/orders list?
The proper way to add new operations is to define them as menu items. Here is a snippet from the payment module, responsible for the payment operation listed in the screenshot:

  // Payment tab on orders.
  $items['admin/commerce/orders/%commerce_order/payment'] = array(
    'title' =&gt; 'Payment',
    'page callback' =&gt; 'commerce_payment_ui_order_tab',
    'page arguments' =&gt; array(3),
    'access callback' =&gt; 'commerce_payment_transaction_order_access',
    'access arguments' =&gt; array('view', 3),
    'type' =&gt; MENU_LOCAL_TASK,
    'weight' =&gt; 10,
    'context' =&gt; MENU_CONTEXT_PAGE | MENU_CONTEXT_INLINE,
    'file' =&gt; 'includes/commerce_payment_ui.admin.inc',
  );


The key part being this line right here:

'context' =&gt; MENU_CONTEXT_PAGE | MENU_CONTEXT_INLINE,


In fact, in most (maybe all?) places where you see this list of operations or tasks in Drupal Commerce 1.x, they will be defined this way. Another example of this being the transaction listing screen. Payment modules can add new contextual menu items for things like credits, captures, etc: