We see more than 50% of the lunar surface from Earth!
Actually, we get to see closer to 60% of the lunar surface because of the Moon's wobble.
This wobble is called libration. The little manic gif below shows this pattern of libration over the course of a lunar cycle. Part of this also sees the Moon get closer (perigee) or further away from us (apogee) in its orbit around the Earth. When the full Moon coincides with its perigee, we get the so-called Super Moon.
For features along the limb of the Moon, libration can make these features more prominent or even disappear behind the Moon.
I have a couple of sketches I've done show a large crater along the limb, Drygalski, one with a favourable libration apparition, and the other during a poor libration.
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There are many significant features that are totally dependent on a favourable libration in order to be seen. If you've ever attempted to track down a particular feature along the limb, and were frustrated in not being able to see it, very likely it was due to that feature having a poor libration apparition. Or a feature you saw once along the limb, pretty much disappearing next time you tried to spot it.
Alex.