It orbits the Sun, so at one time or another it's able to observe any point in the sky.
LOL, Earth orbits the Sun so at one time or another people on this planet can observe any point in the sky. Earth contends with rotation (our days and nights) as well as tilting along its axis (seasons).
No one on this planet can see the entire sky at a given moment but if they repeat observations day after day, month after month, they can see the entire sky. They may need to move north or south for a skyview of places that are below the horizon but that's about it.
Hubble, JWST, whatever have similar limitations. While they are larger, have different wavelength sensitivities, and don't have to contend with atmospheric interference, they function the same as human eyes. Sensors (whether it be a retina or some electronic component) can only record what it detects from the direction it is pointed at.
I am 16 minutes into the New Eye on the Universe episode, I am watching at 1.5x speed, nice of PBS to give that option. So far it is pretty good, very good graphics in it, highly polished video. For only being streamable in 1080p it looks damn near 4k... they don't use YouTube, it's their own in house video thingy. Whoever is running that is top notch, cause it is excellent all around.
PBS is running it.
NOVA is one of the oldest and best science programs on television and has won every single award it is eligible for.
NOVA's production values are first rate and have been that way for decades, nothing new there.
Nature -- which usually airs right before NOVA -- is another venerable and high quality broadcast. The two combined make up the finest two hours of general science programming an American can watch on television every week.