What did my hardwood installer do wrong here?
From what I see...


There is "trash" in the finish
A patch, roughly in the center and running about 75% of the length, was either dry coated or missed all together


The floor needs to be screened ( buffed with a dull sanding screen ) then vacuumed, and finally tack ragged to get the finer particles that a vacuum WON'T get. I prefer to use a lambswool applicator when running urethane, but that's not the only viable method available.

Edit:
I just saw your additional pics. The issue is that the repaired piece of wood didn't have the same "amount" of finish as the surrounding flooring. Typically the first coat of finish soaks in to the material, which closes the grain and prevents any further penetration.

I cannot say as for the arcs you spoke of. But, there are 2 possibilities... 1) Buffer swirls as you suggested and 2) Edger marks

A typical round floor buffer uses 18" screens, so buffer swirls will be closer to that "size". Edger marks are made from the edger, which is the sander used against the walls. A proficient floor mechanic would also scrape the area that was sanded with the edger. There's way too much detail involved to explain here...

Long story short, the patch or patches should get a good brush coat of finish, to build back up to the finish level of the surrounding floor, then the entire floor screened and recoated.

One more thing, running finish at night is the WORST time of day for doing such. Using natural light is the ONLY way to avoid missed or dry spots. I say this because the wet finish pics seemed to be taken at night.