Notice: Undefined index: discount_name in commerce_discount_remove_discount_components() (line 74 of ...

Just a "quick&dirty" solution while we wait the official fix is the following:

function commerce_discount_remove_discount_components($price_wrapper) {
  $data = $price_wrapper->data->value();
  $component_removed = FALSE;
  // Remove price components belonging to order discounts.
  foreach ($data['components'] as $key => $component) {
     if(!empty($component['price']['data'])){
      if ($component['name'] != 'discount') {
        continue;
      }
      $discount_name = $component['price']['data']['discount_name'];
      $wrapper = entity_metadata_wrapper('commerce_discount', $discount_name);
      if ($wrapper->type->value() == 'order_discount') {
        unset($data['components'][$key]);
        $component_removed = TRUE;
      }
    }
  }

File: commerce_discount.module (located: /profiles/commerce_kickstart/modules/contrib/commerce_discount/
I actually added a check if the $component['price']['data'] is empty.

I know this is NOT the prettiest solution, but saved my Weekend! :)

@m.ioannidis solution expressed as a patch.

Though it does not seem to fix the actual issue. Workaround patch attached.

Same error here. Using commerce kickstart 2.0 rc4.

Error appears when adding a product to the cart.
There is a active pricing rule which uses a custom field as discount parameter:

{ "rules_product_discount" : {
    "LABEL" : "Product discount",
    "PLUGIN" : "reaction rule",
    "REQUIRES" : [ "rules", "commerce_line_item", "commerce_product_reference" ],
    "ON" : [ "commerce_product_calculate_sell_price" ],
    "IF" : [
      { "AND" : [
          { "data_is" : { "data" : [ "commerce-line-item:type" ], "value" : "product" } },
          { "data_is" : { "data" : [ "commerce-line-item:commerce-product:type" ], "value" : "product" } },
          { "entity_has_field" : { "entity" : [ "commerce-line-item:commerce-product" ], "field" : "field_product_discount" }
          }
        ]
      }
    ],
    "DO" : [
      { "commerce_line_item_unit_price_multiply" : {
          "commerce_line_item" : [ "commerce_line_item" ],
          "amount" : [ "commerce-line-item:commerce-product:field-product-discount" ],
          "component_name" : "discount",
          "round_mode" : "1"
        }
      }
    ]
  }
}

When i switch the price component type to "base price", everything works ok.
Unfortunately the patch provided in comment 3 doesn't work. I am looking in to this but haven't found a solution yet.

Pushed a fix.