Can my wife have aspirin while pregnant?

Not recommended. Check with and discuss with your obstetrician. There can bee good use of Aspirin during pregnancy and bad use! in general we do not use Aspirin during this time. Needs careful medical guidance.
Possibly. The general recommendation is to avoid nsaids such as aspirin, motrin, anaprox, (naproxen) etc during pregnancy. Actually it may not be unsafe to use these medications in the first two trimesters. However, use of these medications after about 30 weeks can result in serious and potentially life threatening complications for the fetus. We usually discourage use of all nsaid's during pregnancy for this reason.