This effect only becomes significant if you get near the black part of the black hole. For reference, the time advancement difference between GPS satellites (20,200KM) and the surface of the Earth (6,371KM) is about one second in sixty years.
Obviously, the gravity of a black hole is much greater than that of Earth but it is all relative
. The wasn't much size perspective given. The writers seem to favor leaving some of the most important details (like what the Gorn look like) to the viewer's imagination. There were some numbers thrown out, but the context wasn't entirely clear.