Several weeks difference is not too common. How are they calculating your period and how far do you think you are versus what they say you are.
I don't know about several weeks, how far exactly are you talking about? It is possible to have conflicting dates, especially if you have irregular periods or the egg implanted late.
It is possible to get a different date. In fact, this happens frequently. I don't know what you consider to be "several weeks" but it isn't uncommon to be about 2 weeks off on your date. You could have ovulated early or late, or the baby may have implanted late. Also, depending on your cycle length, the due date may not be what is calculated on the standard "OB wheel". As long as the baby is growing and measuring correctly throughout the pregnancy, don't worry about the difference in dates :)