Just how tightly should a humidor close? Should any air circulation occur?

The lid of a humidor should close as tightly as possible, because you are creating a micro-climate with a very specific humidity level inside, one in which the cigars will thrive and the humidifier won't always need to be refilled.

That said, a certain amount of air circulation is quite desirable. The advantages of electronically controlled air humidifiers come to the fore here. The sensors of these humidifiers continuously measure the humidity level and activate a fan which circulates the air inside the humidor at regular intervals.

For humidors with conventional humidifiers, the air is circulated only when the lid is opened, making it quite reasonable to open the humidor occasionally. This prevents the moisture from settling, leading to uneven humidity levels at different points within the humidor.