I mentioned this on the French WP Village Pump and saved a screenshot of a Wikidata item showing what I have experienced sometimes:

• when editing the "mère" (mother) property, I cannot add a qualifier because the "ajouter un qualificatif" (add qualifier) is totally inert as if it was a background image, it does not get underlined under the mouse cursor
• for the "père" (father) property, a qualifier is now present so the situation is a little different, what does not get underlined is the "supprimer" (remove) positioned like in the previous case at the first line below the property value, though sometimes I can find a very narrow vertical zone in the downward leg of the "p" where the cursor makes it underlined and working

Now I see that the [?] tooltip giving instructions about the property value is fully over the "+" of "ajouter un qualificatif" for "mère", and almost fully over the "trash can" icon of "supprimer" for "père", so I suspect the root of the problem is a bad position of this [?] which does not allow to edit Wikidata properly whenever it happens.