Even more baffling is the concept of a "night shift" on a spaceship. The lights are dimmed for the night shift in "Data's Day," and Dr. Crusher has the bridge during the night shift in "Thine Own Self," but how did they pick which eight-hour segment of time would be "night"? It's not even night at the same time everywhere on Earth; did they pick an official time zone for the Federation and go with it? Does that zone observe daylight saving time? Assuming that the organization of shifts and light levels is an effort to cater to humans' circadian rhythms, what happens to crew members who aren't from Earth? That would mean the Betazoids, the Klingons, and all the other nonhuman crew are left downing Red Bulls and snorting Adderall just to keep up.
Weeks And Months
Like days, weeks and months only work if you're on Earth. Imprecise as they are, stardates definitely aren't based on Earth's system of seven-day weeks and 30ish-day months, so why do crews still use that calendar?