Hi,
Do you have enabled the "multi cart" option in Configuration > Features > Wishlist ?
When adding to wishlist, you must be logged in on the website, once logged in, a message is displayed informing that the product has been correctly added to the wishlist.
To mark the wishlisted products in a listing, you can edit the view "product / listing_img_title" (or another one based on your settings) and in that view add PHP code to get the content of the cart and then display an icon or not based on the product id and its presence in the wishlist. This require PHP knowledges.