Midnight on a Full Moon

Midnight would depend on the time zone. For instance, when it is exactly midnight in London, it a few minutes later in Wales.
The moon may have some significance in magic, I cannot see how midnight does.

I also recognize midnight through 3 am as the witching hour.
However the powers attributed to casting spells at this time is because it is a inbetween time because of the exact lack of clarity that occurs during the 12:00 hour it's between the day you live in and the next one and as you already know in between times are very powerful when casting magic much like casting spells near halloween. Also much like halloween since midnight is the inbetween hour in many places youll find that spirits and other metaphysical entities are more easy to contact or are more active because it is easier for them to manifest during this hour of uncertainty.