#2 Accepting too large of a delivery window. Many companies will tell you your items will be delivered anywhere from 2 to 6 weeks of your desired move-in date. That leaves you in a new city without any of personal belongings. Try and look for a moving company who can give you an exact day arrival time. This should eliminate this problem completely.
#3 Contacting only one nationwide mover. When moving your most valuable possessions across the country you want to make sure you get the best service. Getting multiple quotes will allow you to get the best possible service that will allow your move to go smoothly. Be sure to look at other factors besides price ask about insurance and make sure they are legally able to travel across country. Make sure to look at reviews, yelp is normally a great source.