Hi,
You basically need to turn on the "show description" option for all your listing menus. However, On your last link, you can see the parameter "Itemid=134". It means that joomla didn't find a menu item with the id 134 and thus there is no "show description" option for that page since there is no existing menu item attached to it.
That link comes presumably from a module where the "menu" option is set to a a menu item 134 which doesn't exist (or is not valid) anymore. So you should go in the menu Display>Content modules, edit your modules and make sure that their "menu" option is set to a category listing menu item like the one with the id 165. Then, the links of these modules won't contain the "Itemid" parameter and the show description option of the menu selected in the module will be taken into account.