Seasonal Movement
Constellations move with the seasons. Which constellations are viewable in different places, at different times of the year, are regulated by how the Earth faces the sun during its orbit. The Earth is always tilted at 23.45 degrees, and regardless of where it goes around the sun, it remains in that tilted position. This tilt gives the Earth its seasons. It also means that the constellations, though moving in a circle around the Earth, are in different places at different times of the year -- and some of them vanish from sight entirely.
Hemisphere Differences
Not every hemisphere can see the same set of constellations. The Equator and Prime Meridian each divide the Earth into four hemispheres: north, south, east and west. Each of those areas will see its own set of constellations, and will therefore navigate regarding them. Should someone cross into another hemisphere, he will have to learn the important constellations and stars to use there or be lost. The Northern Hemisphere looks for Polaris (the North Star), Cassiopeia and Ursa Major and Minor (the Big and Little Dippers). In the Southern Hemisphere, they use the Southern Cross.
Wobbling Earth
Another consideration when thinking of navigation by the stars is perhaps lesser-known. The phenomenon was discovered in 1891 by Seth Carlo Chandler Jr., who gave his name to the event: the Chandler Wobble. More than 100 years later, the mystery of why was solved by Dr. Jeff Gross. This wobble would have moved the axis of the Earth a good 6.5 meters at the North Pole, which in turn would effect how navigators used the stars to get exactly where they needed to go.
Night Travel
Finally, common sense dictates a disadvantage. Traveling at night is difficult enough without light to see by, and using constellations requires travel at night. As well, in some areas of the world, during some parts of the seasons, such as in Alaska, it never gets dark enough to see the stars for months at a time. In and around huge cities, the ambient light the city gives off makes it nearly impossible to spot any but the brightest stars, let alone factoring in cloud cover or pollution agents to obscure the view.