One of the family of errors that gets to me is celestial mechanics—the structure of the earth, moon, sun, and universe as a whole, and how they work together. The day I learned that not everyone grasps basic lunar-planetary astronomy was the day I watched Catwoman, a movie reviled by many, but here's where it lost me.
The art designer for the movie decided that the iconic look of the movie would be Catwoman and the cityscape silhouetted against a giant full moon on the horizon. So that shot was included—when Catwoman was out prowling in the middle of the night. And when Catwoman went out again a few nights later. Full moons don't work like that!
A full moon occurs when the moon is exactly opposite the sun. So during a full moon, the moon is rising up over the eastern horizon when the sun is going down over the western horizon—180 degrees apart from each other. By the middle of the night, the sun is on the far side of the earth and the full moon is overhead. Around dawn, the sun will be coming up over the eastern horizon and the full moon will be setting.
The moon takes approximately 28 days to go through its cycle. It is actually full, rising exactly at sunset, for one day. The night before the full moon, it looks almost full, and rises a little bit before sunset. (Pro tip for photographers and videographers: this is a great time to capture a dramatic looking moon while the scenery is getting a little more light from the setting sun.) The night after being full, the moon rises a little after sunset. Each succeeding night it rises later and later, getting skinnier and skinnier as we see the light of the sun hitting it side on.
Fourteen days after full, it's the new moon—we don't see it at all because it is between the sun and us and only the shadow side is facing us. Before the new moon, we only see a sliver of crescent coming up just before sunrise and setting just ahead of the sun at sunset. After the new moon, a sliver of crescent follows the sun after sunrise and dips below the horizon ahead of the sun at sunset. The moon and sun then pull progressively farther and farther apart, the moon growing fatter, until the next full moon.
So when you are writing werewolf fic, the pack does not have to wait around wondering when the full moon will rise—they know it will be up at sunset, and will be up all night.
For the phase on any given date or stretch of dates, use a moon phase calculator like StarDate's. The site also has useful diagrams and information explaining moon phases.
East, West, and Time Zones
Picture a globe on a stand. The earth has been divided into hemispheres of north and south, with the equator at the widest part of the sphere. We call Eurasia, Africa, and Australia the Eastern Hemisphere and the Americas the Western Hemisphere, but east and west are actually relative. Globes on stands can be spun either way, but in reality the earth spins east to west. The sun rises in Japan before it rises in Turkey. The sun rises in Kenya before it rises in Morocco. The sun rises in New York before it rises in San Francisco. And by the time it rises in New York, it's already been up in London for five hours.
For most of history, people kept time where they lived by sunrise, sunset, and noon. Traveling by foot, horse, or ship to another location was slow enough that a traveler just adapted to the destination's timekeeping. However in the 19th century, telegraphs set up instant communication and trains gave us rapid travel. Railroads had a vested interest in people knowing when a train would be boarded, how long it would travel for, and when it would arrive. The United States eventually codified four time zones, and soon after the world divided into 24 time zones.
This makes it fairly easy to calculate the time in different places, once you look up the time difference. If Dom is in Los Angeles at 8:00 p.m. and he calls Ariadne doing a job in Boston, he'd better have an apology ready for disturbing her at 11:00 at night. Likewise, Ariadne should not be calling back first thing in the morning, when 8:00 a.m. for her equals waking up Dom's kids at 5:00 a.m. in California.
Because we use these manmade time zones to delineate an hour at a time, there are natural consequences. Captain Jack in London could text Ianto in Cardiff what a beautiful sunset it is, and sunset is half an hour away in Wales, even though they're in the same time zone. Likewise, 12:00 noon rarely falls when the sun is exactly overhead, as there is considerable territory east and west of "solar noon" captured within any given time zone.
Time can go back and back and back only so far as you keep going west. Eventually you hit the International Date Line in the middle of the Pacific Ocean, marking where a day begins. On any given date (counting larger land masses rather than small Pacific islands), the sun rises first over New Zealand and eastern Russia and rises last over Hawaii and Alaska's Aleutians Islands. Even though it wouldn't take long to get from Alaska across the Bering Sea, and a phone call between the two would only seem to be two hours different, Q, on a US Air Force base in Shemya, Alaska, calling at 10:00 a.m. on November 30 would reach Bond in Kamchatka at 8:00 a.m. December 1—two hours behind, because Russia is west of Alaska, but a day ahead because Russia is on the west side of the International Date Line. You would more accurately say that Q is 22 hours behind Bond.
The last thing to know about time zones is that many countries or regions observe Daylight Savings Time (DST). The residents "spring ahead" their clocks one night in the spring (meaning they lose an hour of sleep because wake up time comes earlier, or they come in late to work because they forgot to make the change) and "fall back" an hour with their clocks, back to Standard Time, one day in the fall (gaining an hour of sleep). This usually doesn't affect your stories much because most countries will all move their clocks together. (Don't forget that in the Northern Hemisphere the spring ahead is generally around March and the fall back is around October, while in the Southern Hemisphere it is the opposite. See next section.)
However in the United States, Arizona and Hawaii do not observe DST. During spring or summer, that phone call from Q to Bond described above would be three hours (or 21 hours) different since Kamchatka doesn't observe DST. Different countries choose different dates for springing ahead and falling back, so a usual four hour difference might be five for a week or two. Some regions move a half hour, or other odd increment. At different times in history, especially during wartime, all different kinds of hours have been set. If your story includes a time difference worth mentioning, you may want to double check your dates for what that time difference is.
There are a lot of resources and articles on time zones, world times, sunrise and sunset times, and more at timeanddate.com.
North, South, Seasons, and the Ecliptic
The major difference between the Northern Hemisphere and the Southern Hemisphere is that their seasons are opposite. Because of the tilt of the earth, when the Northern Hemisphere is pointed towards the sun and getting summer warmth, the Southern Hemisphere is pointed away and it's winter. When the earth is at the other swing of its orbit, it's vice versa. Miss Fischer enjoys a very green Christmas in Melbourne, thank you very much, as did the crew filming the Lord of the Rings and Hobbit movies in New Zealand.
Another difference between the hemispheres is that north of the equator the sun rises in the east, swing across the sky south of straight overhead, and sets in the west. South of the equator, the sun travels a northern path between east and west. This path is called the ecliptic.
The solar system is essentially flat. It's not a perfect two-dimensional disc—the paths of the planets' orbits go somewhat higher and lower in relation to each other. The moon also follows the same general plane around us as the earth and the planets follow around the sun. So if you drew a line in the sky showing the sun's path during the day, along that general band is also where you'd see the moon's path at night, and where you'd see any visible planets. The twelve constellations chosen to be the zodiac are the constellations along the ecliptic, and early astronomers would track the progress of the moon and planets across their steady backdrop.
As you might guess from the name, the ecliptic is where eclipses happen. The moon's orbit isn't always in an exact plane with the earth and the sun. But when the moon is full and it is exactly on the other side of the earth from us, we see the shadow of the earth go across it—a lunar eclipse. During a new moon, if the moon happens to be passing directly between us and the sun, we get a solar eclipse. Both kinds of eclipses impact part of the world, but not all. At any given time, half the earth is facing the wrong direction to see anything at all. And the moon being small and the paths not being perfect, they cast a partial shadow, or partial eclipse, unless you happen to be directly under the path of the orbit's shadow.
The path of the sun, moon, and planets depends upon how close you are to the equator or the poles. Around the equator, the sun is high in the sky at noon. As mentioned above, north of the equator, the sun curves to the south as it moves across the sky, as do the moon and planets. When Constable Ben Fraser is in woods rather than tundra, he can look for moss on trees to find which way is north—the sun never hits the north side of the trees. (Or he can just look at his shadow at noon.) Towns tend to build on the sunny south slopes of hills, cats curl up in sunny south-facing windows, and people escape to the north side of a wall to get out of the hot sun. South of the equator, everything is the opposite. The sun (and moon and planets) travel a northern path, noontime shadows point south, and north equals sunny and warm.
The farther north you go or the farther south you go, the lower in the sky the ecliptic passes. During summer in the north, the sun rises earlier and towards the northeast, and sets later and towards the northwest. During winter the sun rises later and towards the southeast and sets earlier towards the southwest. In the Southern Hemisphere the directions are the opposite—the sun rises and sets more southerly in summer and northerly in the winter. Again, check those sunrise and sunset times at timeanddate.com.
At the Arctic Circle, the summer sun rises and sets so far north that, well, it is north, and it never actually goes below the horizon. It travels around in a circle, dipping towards the northern horizon at midnight and moving higher in the southern sky at noon. During the winter, the sun travels around just below the horizon, but never manages to rise. Here is a good diagram of the ecliptic at the Arctic Circle. At the Antarctic Circle the situation is much the same except that the sun is highest in the north and lowest in the south, and the midnight sun is in December while the winter dark is in June.
The Astronomy section of bluewolf458's feature on Geography has more great tips on writing the sky and daylight for various locations.
Your readers will come from all over, likely including where you're writing about. Try to not get their details wrong!
StarDate—moon phases, constellations, eclipses, sunrise and sunset, and more
timeanddate.com—time zones, world clock, calendar, weather, sunrise and sunset, and more