JWST doesn't actually stay right in L2 (which is in Earth's shadow). Instead it orbits around L2 about twice a year in a halo orbit, with a radius large enough that it can have nearly constant access to solar power (I do not know if it fully avoids the moon's shadow). You can see a good animation near the top of https://www.jwst.nasa.gov/content/about/orbit.html
Awesome link. Thanks for posting. I'm wondering, does anyone know why we didn't send JWST to L4 or L5, where (as mentioned in the link above) it could remain orbiting indefinitely without the need for fuel? Is it because those points are a lot harder to get a spacecraft to?
JWST is making observations in orange to mid-infrared wavelengths. The sun, earth, and moon are all quite hot and emit a lot of light in that range of wavelengths. Near L2, JWST can use one sunshield to block out light from all three bodies, with less impact on what portion of the sky it can observe
What other errors did you find?