Fullstory captures dropdowns, but cannot capture native dropdowns (i.e., <select></select> ) as they’re being changed, because these changes don't cause DOM mutations, so we're unable to capture and render their contents. Fullstory watches for events and for page mutations (more on how Fullstory works here), but the display of the dropdown isn't actually a mutation of the page.
You may have noticed that you do get to see the change as the user selects a list, and you can inspect the DOM of the playback page if you really need to see the option list (in HTML), but we haven't found a way to visually display this in playback.