Here's what I wrote up for my flat world, modeled onthe order of the stick comic (stick figure physics, not the same world cosmology).
Cosmology
The world is called "Eurastika" by its denizens. The world is flat, with a wrap-around characteristic, should one travel the 26,000 miles to find out. The sun is a light source that resides 20,000 miles above the plane. The sun travels a path from East to West across the equator of the world (the middle as determined by the path the sun takes). It exists in all positions along the equator at the same time. (a dilema for whoever discovers quantum physics in this world to solve). Thus, from any position on the ground, it appears that the sun rises and sets. It also will be "midnight" at the same time, anywhere on the plane. The day/night cycle is 24 hours. The plane tilts along the equatorial axis seasonally, which causes the seasons, temperature variance, and varying length in daylight hours.
Eurastika has a single moon that travels diagonaly across the equator from a north-east to south-west direction. this causes it to appear in varying positions across the world. The moon exists as normal entity, and truly does appear different when viewed at the same time from different places.
[edit]Science Content
The sun appearing in all positions along the equator is a quantum physics effect. Basically, the sun exists in such a state that it hasn't determined it's starting position, and thus exists in all posible starting positions along the equator. It's momentum keeps it moving, so it effectively shifts position along the equator. The sun is not a big entity, being close enough to the plane provide its warmth. It is still hot enough that if one were able to travel to it, proximity would be fatal.
The wrap-around effect isn't really scientific, you might claim it as a curvature of space problem. However, the plane really is flat. When sailing, ships on the horizon are just really tiny, as opposed to only being able to see the crow's nest, as the rest of the ship is obscured.
The plane tilt will cause seasonal effect farther away from the equator, because as the plane tilt brings the northern half closer to the sun, getting it more heat. Technically, there's a little problem with what happens to the southern half, since it is technically, just north of the northern half, if you get our meaning. Somehow it all works out though. Perhaps the wrap-around effect only works east-west, and not along the northern/southern borders. it's too cold there to find out.
The last problem to solve is the whole distance of the sun to the plane, size of the world, and the appearance of night (aka lack of visible sunlight). Since the world isn't round, the sun can't hide behind the other half. If the world width is very wide, and the sun height is not very high, then as the sun recedes from your position, it will be mostly obscured from view due to the landscape. At most, there will be a glow on the horizon all night.