What do the red and blue tiles on the map mean?
Solution 1:
Red is the location of creatures and monsters, the red meaning "potentially dwarf-scaring or -mauling". Blue is the location of your dwarfs.
The colour ignores z-levels of air, so if there are fliers you'll have to hunt through the elevations to find out what the map is indicating. Also note that there is no consistent size relationship between you normal view and the map, so you might be looking at multiple map-squares or just part of one, depending on your screen size and the size of the embark area.