You cannot move a card on a cardboard because you do not have permission to edit the issue. To fix this, you must change the tracker settings. Another reason is because there are no workflow transitions for the current status of the card.

Read-only cards are marked with a little pin icon, with a tooltip telling you why you cannot move them.

After a card is dropped, if its tracker has required fields, you must set those when updating the status. Therefore, after dropping such cards, you can get an issue editor overlay window to ensure all required fields are set properly.