Insomnia
A nearly immediate effect of going to bed after midnight is that it throws off your natural circadian rhythms, governed by your SCN, and this may lead to insomnia. As well as having a harder time falling asleep, you will also have trouble staying asleep. Even if you have a schedule that allows you to wake later, the rest of the world will not readily ACCOMMODATE you. Often, the noise and commotion of the day will in all likelihood wake you before you wish; it is a well-documented fact that night shift workers, despite having a schedule that allows for an adequate amount of sleep, get less sleep than those who work days.
Along with anxiety, a whole host of negative consequences flow from this basic fact of sleep deprivation.