Job market is steadily growing. There is a lot of new commercial construction going on, much of it speculative.
Right now it's a buyers market for homeowners; there has been a flood of new home construction over the last five years, to the point that the local market is a little bit saturated.
The big thing in Anchorage is whether or not a natural gas pipeline gets built from the North Slope to either Valdez or Canada. If that happens, Anchorage's economy will boom again. If not, look for the market to continue its slow, steady growth pattern.
Cost of living is higher in Anchorage than most of the country, save some of the major metro areas like New York or San Francisco. This is due to the geographic isolation. Here's a good website for comparing the cost of living from one city to another:
http://cgi.money.cnn.com/tools/costo...tofliving.html