Most likely you can solve this "error" with a correct styling in your CSS-file. Hit F12 and highlight the element blocking your drop-down and set
overflow attributes to correct values.
But my first test would be to add
display: block; to the element blocking the drop-down and see what effect you get from that action.
A final tip: customizing CSS is hard in SharePoint and you might have to use
!important as an extra attribute to every style change you try to accomplish. But that applies only when you already have a solution full of important statements. In all other cases, important should be avoided.