I have a puzzling question about the moon face, please pick apart my reasoning.

A few months ago I saw the moon out during the day time, and I asked my gf how could that be if others are seeing the same moon? This is a pretty common question, but I've had this diagram in my head that shows me this does not make sense.

To first even consider my drawing, I need to know one definitive answer: can two people on opposite ends of the world see the moon at the same time? I've seen a lot of discussion, but nobody has seemed to confirm this through any experimentation.

For sake of argument, the two perspectives on my round Earth are not on exact opposite ends, but slightly less than 180 degrees. I'm assuming* that if those two locations are equally opposite distances from the Moon than they would both be cloaked in darkness, at least enough to see the moon.

What puzzles me, is how can they see the same face of the moon? I mean, they would surely see different sides of the moon. I feel like I must be grossly simplifying this, or am completely missing something here.

Can anyone shed some light on this? If I'm being illogical in my thinking I'd like to know where I'm going wrong.

They do see slightly different faces, but the moon is MUCH farther away than shown in your picture. 

I'm assuming the principal still stands regardless of the distance of the moon. So, what you're saying is that we've seen more than 50% of the moon?

I'm assuming the principal still stands regardless of the distance of the moon. So, what you're saying is that we've seen more than 50% of the moon?

Yes, but that's more due to the moon's libration than the earth's rotation, and I'm not counting views from spacecraft. 

Here is a simulated image of the moon's libration:

Is that rendered? Very interesting. I'm not aware with libration.

So, if those two perspectives were to take a snapshot of their view of their moon at exactly the same time their pictures would be different? (showing different sides of the moon?)

Is that rendered? Very interesting. I'm not aware with libration.

So, if those two perspectives were to take a snapshot of their view of their moon at exactly the same time their pictures would be different? (showing different sides of the moon?)

Slightly different.  In Stellarium, I can focus on the moon and fast-forward time to see how the view of the moon changes each day.  You might want to get it and try it out. 

Sounds interesting, but I'm more interested in real world tangible results. Not graphic renderings based on programs that operate on the assumption of what I'm trying to figure out(if earth/moon is flat or not).

Actual images. 

Is that rendered? Very interesting. I'm not aware with libration.

So, if those two perspectives were to take a snapshot of their view of their moon at exactly the same time their pictures would be different? (showing different sides of the moon?)

Should do research before posting.

Yes if two people in different locations took a picture of the moon they would see ot from slightly different angles, we do see more than 50% of the moon.

Like Blue Moon said, the moon is to far away to notice with the naked eye.

Is that rendered? Very interesting. I'm not aware with libration.

So, if those two perspectives were to take a snapshot of their view of their moon at exactly the same time their pictures would be different? (showing different sides of the moon?)

As far as I am aware the "video" of libration is from a sequence of photos taken over a period of time.
You can read a lot more on lunar libration in How much of the moon can we see from Earth?

The difference in views of two people as far apart as possible on earth can be seen from this scale diagram of the earth moon system:
The angle difference is about 2°, so these observers would hardly notice the difference.