genetic defects would eventually infect such a small population
Unless they were continually screened and had genetic repairs performed on them during the mission.
Keep in mind that they will be in a highly radioactive (by earthly standards) enviroment.
of course, if the ship is sent on an only 3 or 4 generation trip, then the risk of genetic defects appearing in the population would be less than if it were a 10 or 20 generation trip.