It's a real pain having to go each port just to check your influence on each one of them specially if your trying to take over a port for your nation.
Now i want to suggest a better and faster way of seeing your influence in all port all at the same time.
You can add either an extra page for this but that would be a lot of hardwork so maybe you can just add it in at the "Active Port" page. Where it shows all the port you have warehouses and stuff. Have it either in between the port and population or stick it in at the end.