Hello Francesca,
Are you using your own skin? Can you try with standard skin and see if the issue persists?
If you are using standard Default skin, the source of the dropdown list icon is "/SAP/BC/BSP/SAP/thtmlb_styles/sap_skins/default/images/down.gif". To get this information, you can use F12 Developer Tool of IE. Then you open the BSP application thtmlb_styles using TCode SE80, go to Mimes -> sap_skins -> default -> images, you will see the down.gif file.
So please use the F12 to get the source of the dropdown list icon where the issue happens and then check if the image is missing using SE80. If it is missing, you need to add the image.
Best regards
Abby Ding