When I look at the night sky I seem to resolve points which are local stars and milkiness at further regions of the galaxy. But what is between? I think there must be a lot of stars which are too faint to see individually, and yet not perceivable as part of a dense region of stars. Is this at all accurate? Does anybody know how much we fail to see when we think we are looking?
Even the Hubble telescope cannot "see" many of the stars and galaxies in the dark parts of space at first glance. If they fix the Hubble on a dark patch for several days, the photons from extremely distant stars and galaxies will fill the image.
Also, the Earth's atmosphere will obscure and distort many stars that are visible from low Earth orbit and beyond. Astronauts can see many more stars than we can.
Regarding your question, "how many are we missing", that's a tough one to answer. It depends on what level of detail you are talking about.
I am not quite sure if i understand your question correctly. But I think the answer to your question is:
It depends on where you stand and look into the sky.
Light pollution is the biggest issue observing anything in the sky. If you are out in the night in a big city you just see a few stars (at a clear night). The further you are away from any light source the more stars you are able to see with eyes only.
According to Wikipedia,
Theoretically, in a typical dark sky, the dark adapted human eye would see the about 5,600 stars brighter than +6m while in perfect dark sky conditions about 45,000 stars brighter than +8m might be visible.
(By the way, "+6m" means stars of apparent magnitude 6 or brighter.)
Under the best conditions, a person could see 45,000 stars. That's quite a lot. However, the Milky Way alone has over 200 billion stars (and that's a low estimate!). So we can only see a small fraction of the total stars in the Milky Way. Earth-based optical telescopes can do a lot better, though.