The name of the game in 23.98p.
Your video monitor is not broken. At 1080 23.98p the screen will exhibit a flicker artifact more visible in bright scenes. It is a product of a relatively slow frame rate. Flicker sensation is more enhanced if you place the TV in your peripheral vision. While unpleasant this artifact is easy to get used to.
720 59.94p will not show any flicker even when shot in Varicam in 23.98p mode. The reason is that the actual frame rate of the format is roughly 60 pictures a second which is high enough to trick the brain into not seeing flicker.
The viewers at home are not likely to see the flicker because HD in the U.S. is broadcast as either 1080 59.94i or 720 59.94p.