The Earth and the Moon do interact, but because they have different sizes and masses the effect on each is different.
The Moon rotates once in its orbit around the Earth, causing it to constantly show the same face. This was the Earth's effect on the Moon due to tidal dragging by gravity.
It's pretty stable, the Moon will continue to show the same face to the Earth even as the tidal forces cause it to orbit farther and farther away.
We actually see slightly more than 50% of the Moon. The Moon's orbit causes its aspect to nod because its orbit is slightly elliptical and shimmy because it's not orbiting directly over the equator. Over time we actually see almost 60 percent of the surface of the Moon (an effect called libration).
The Moon's effect on the Earth has been to slow its daily rotation to 24 hours. In the past, the Moon was much closer to the Earth, and the day was much shorter. As time passes and the Moon moves into a wider orbit, the length of the Earth's day will increase (see e.g. this Scientific american post).
I've read that the Moon would recede to a certain point, then begin approaching the Earth again, but unfortunately the Sun will swell into a red giant before then and swallow the Earth and the Moon.
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